This video just wasn't very helpful moving forward because it only gave the answer and steps to answer one specific problem rather than a clear formula for many different problems. Does anyone know the explicit and recursive formulas for geometric sequences, or could someone direct me to another video that I'm not seeing that would be more helpful? Thanks.

This video explains both explicit and recursive formulas for _geometric_ sequences: https://www.khanacademy.org/math/algebra/sequences/constructing-geometric-sequences/v/explicit-and-recursive-formulas-for-geometric-sequences These videos explain recursive and explicit formulas for _arithmetic_ sequences: https://www.khanacademy.org/math/algebra/sequences/constructing-arithmetic-sequences/v/recursive-formula-for-arithmetic-sequence https://www.khanacademy.org/math/algebra/sequences/constructing-arithmetic-sequences/v/explicit-formulas-for-arithmetic-sequences And these videos explain how to convert between the two: https://www.khanacademy.org/math/algebra/sequences/constructing-arithmetic-sequences/v/recursive-formulas-for-arithmetic-sequences https://www.khanacademy.org/math/algebra/sequences/constructing-geometric-sequences/v/converting-an-explicit-function-to-a-recursive-function Hope this helps!! :)

when i raise -1 to the 4th power in my calculator i get -1.Something wrong with my calculator?

Make sure u have entered it correctly. If you enter just -1^4, then the calculator will read it as 1 raised to 4th power multiply by -1 i.e. -1. If you want to do -1 to the 4th power then you should enter (-1)^4. you should get 1.

is this an example of recursive sequence?

The video that immediate follows this one covers recursive formulas for a geometric sequence.

When I solve word problems, they're are not just n-1 for the exponent but also n. When do you put n-1 and n? What do they mean? That's what I don't get. Thank you for the help.

n stands for the *N'th* number in a geometric series. It is very important that you know where the geometric series start, often denoted as *a*. 1) If the series contains a fixed part and a variable part, it is often n-1. E.g. You have 50 euro's in January (month 1) and you add 20 every month. How much do you have in July (7th)? In this case, the *first* addition is in February, which is month 2. Therefore, we need to subtract 1 from the 'the month number'; so it becomes 50+20(n-1) (Note: 30+20n works as well but is not logical to start off with 30). 2) If the first term is part of a larger series; like 3,9,27,81,243,729. The formula 3^n would make sense. Since the first number is n=1 (in math we often start at 1; in coding usually at 0), 3^1=3 is correct.

so for n are always going to plug in 5 for n

No, you put in whichever term in the sequence it is. If you are trying to find the 7th one you plug in 7.

Main content

Algebra 1

Course: Algebra 1 > Unit 9

Lesson 3: Introduction to geometric sequences

Using explicit formulas of geometric sequences

Name: Using explicit formulas of geometric sequences
Uploaded: 2016-03-17T03:15:05Z
Description: Sal finds the 5th term in the geometric sequence whose explicit formula is 3(-¼)^(i-1).

CCSS.Math:

HSF.IF.A.2

HSF.IF.A.3

Google Classroom

Sal finds the 5th term in the geometric sequence whose explicit formula is 3(-¼)^(i-1).

Want to join the conversation?

Sort by:

DecentMakeover
Posted 6 years ago. Direct link to DecentMakeover's post “when i raise -1 to the 4t...”
when i raise -1 to the 4th power in my calculator i get -1.Something wrong with my calculator?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Sneha Kumar
  Posted 6 years ago. Direct link to Sneha Kumar's post “Make sure u have entered ...”
  Make sure u have entered it correctly.
  If you enter just -1^4, then the calculator will read it as 1 raised to 4th power multiply by -1 i.e. -1.
  If you want to do -1 to the 4th power then you should enter (-1)^4. you should get 1.
  Comment on Sneha Kumar's post “Make sure u have entered ...”
  (17 votes)
Grace Sheldon
Posted 6 years ago. Direct link to Grace Sheldon's post “This video just wasn't ve...”
This video just wasn't very helpful moving forward because it only gave the answer and steps to answer one specific problem rather than a clear formula for many different problems. Does anyone know the explicit and recursive formulas for geometric sequences, or could someone direct me to another video that I'm not seeing that would be more helpful? Thanks.
Button navigates to signup pageComment on Grace Sheldon's post “This video just wasn't ve...”
(4 votes)
Answer
- ℳ𝒶𝒹ℯ𝓁ℯ𝓃𝒶 ℬ𝒾𝒸𝓀𝓁ℯ𝓎
  Posted 6 years ago. Direct link to ℳ𝒶𝒹ℯ𝓁ℯ𝓃𝒶 ℬ𝒾𝒸𝓀𝓁ℯ𝓎's post “This video explains both ...”
  This video explains both explicit and recursive formulas for geometric sequences: https://www.khanacademy.org/math/algebra/sequences/constructing-geometric-sequences/v/explicit-and-recursive-formulas-for-geometric-sequences
  
  These videos explain recursive and explicit formulas for arithmetic sequences:
  
  https://www.khanacademy.org/math/algebra/sequences/constructing-arithmetic-sequences/v/recursive-formula-for-arithmetic-sequence
  
  https://www.khanacademy.org/math/algebra/sequences/constructing-arithmetic-sequences/v/explicit-formulas-for-arithmetic-sequences
  
  And these videos explain how to convert between the two:
  
  https://www.khanacademy.org/math/algebra/sequences/constructing-arithmetic-sequences/v/recursive-formulas-for-arithmetic-sequences
  
  https://www.khanacademy.org/math/algebra/sequences/constructing-geometric-sequences/v/converting-an-explicit-function-to-a-recursive-function
  
  Hope this helps!! :)
  Comment on ℳ𝒶𝒹ℯ𝓁ℯ𝓃𝒶 ℬ𝒾𝒸𝓀𝓁ℯ𝓎's post “This video explains both ...”
  (8 votes)
dena escot
Posted 10 months ago. Direct link to dena escot's post “is this an example of rec...”
is this an example of recursive sequence?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Kim Seidel
  Posted 10 months ago. Direct link to Kim Seidel's post “The video that immediate ...”
  The video that immediate follows this one covers recursive formulas for a geometric sequence.
  Comment on Kim Seidel's post “The video that immediate ...”
  (3 votes)
korean_default
Posted 3 years ago. Direct link to korean_default's post “When I solve word problem...”
When I solve word problems, they're are not just n-1 for the exponent but also n. When do you put n-1 and n? What do they mean? That's what I don't get. Thank you for the help.
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Timo
  Posted 3 years ago. Direct link to Timo's post “n stands for the *N'th* n...”
  n stands for the N'th number in a geometric series.
  It is very important that you know where the geometric series start, often denoted as a.
  1) If the series contains a fixed part and a variable part, it is often n-1. E.g. You have 50 euro's in January (month 1) and you add 20 every month. How much do you have in July (7th)? In this case, the first addition is in February, which is month 2. Therefore, we need to subtract 1 from the 'the month number'; so it becomes 50+20(n-1) (Note: 30+20n works as well but is not logical to start off with 30).
  2) If the first term is part of a larger series; like 3,9,27,81,243,729. The formula 3^n would make sense. Since the first number is n=1 (in math we often start at 1; in coding usually at 0), 3^1=3 is correct.
  Comment on Timo's post “n stands for the *N'th* n...”
  (2 votes)
r.ornelas3
Posted a year ago. Direct link to r.ornelas3's post “I dontunderstand how to f...”
I dontunderstand how to figure them out
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
Rodriguez, Malik
Posted 3 years ago. Direct link to Rodriguez, Malik's post “why didnt he multiply the...”
why didnt he multiply the 3 to 256
Button navigates to signup pageComment on Rodriguez, Malik's post “why didnt he multiply the...”
(1 vote)
Answer
cmw89123
Posted 5 months ago. Direct link to cmw89123's post “When I put this into my c...”
When I put this into my calculator, it showed the answer, but it was negative. I need to know if I have done something wrong.
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Kim Seidel
  Posted 5 months ago. Direct link to Kim Seidel's post “You likely typed in: -1^4...”
  You likely typed in: -1^4 when you needed (-1)^4.
  You need to parentheses to indicate that the base of the exponents is the negative number. If you don't use the parentheses, then the base is a positive value and the "-" is applied after the exponents.
  
  Hope this helps.
  Button navigates to signup page
  (1 vote)
carmenleah
Posted 4 years ago. Direct link to carmenleah's post “I got a problem that went...”
I got a problem that went like
c(n)=4/9(-3)^n-1
trying to figure out the third term in the sequence
4/9(-3)^3-1 to 4/9(-3)^2 = 4/9*6 =2.66...
but the hint said that the answer was 4 and that would need the exponent to be 3. Why didn't the subtract the exponents?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Kim Seidel
  Posted 4 years ago. Direct link to Kim Seidel's post “The error is in your mult...”
  The error is in your multiplication.
  (-3)^2 = (-3) times (-3) = +9, not 6
  Hope this helps.
  Comment on Kim Seidel's post “The error is in your mult...”
  (1 vote)
philile mnyakeni
Posted 3 years ago. Direct link to philile mnyakeni's post “how did you get the answe...”
how did you get the answer
Button navigates to signup pageComment on philile mnyakeni's post “how did you get the answe...”
(1 vote)
Answer
Mia Abeyta
Posted 4 years ago. Direct link to Mia Abeyta's post “so for n are always going...”
so for n are always going to plug in 5 for n
Button navigates to signup pageButton navigates to signup page
(0 votes)
Answer
- redtrombone
  Posted 4 years ago. Direct link to redtrombone's post “No, you put in whichever ...”
  No, you put in whichever term in the sequence it is.
  If you are trying to find the 7th one you plug in 7.
  Button navigates to signup page
  (2 votes)

Video transcript

- [Voiceover] The geometric sequence A sub I is defined by the formula and so they tell us that the Ith term is going to be equal to three times negative one fourth to the I minus one power. So given that, what is A sub five, the fifth term in the sequence? So pause the video and try to figure out what is A subscript five? Alright, well, we can just use this formula. A... A sub five is going to be... is everywhere I see an I or a place with a five is going to be equal to three times negative one fourth to the five minus one power. Well that's equal to three times negative one fourth to the fourth power. Well that's going to be equal to... lets see, we're raising it to an even power so it's going to give us a positive value since we're gonna be multiplying the negative an even number of times so it's gonna be a positive value so it's gonna be three times... let's see, one to the one fourth is- oh, one to the fourth power is just one, and then four to the fourth power... let's see, four squared is 16, so four squared times four squared is four to the fourth so it's 16 times 16 is 256. 256. And once again I know it's going to be positive because I'm multiplying a negative times itself four times, or I'm multiplying four negatives together, so that's going to give me a positive value. So I get three over 256. And we're done. That's the fifth term in our sequence. Positive three over 256.