# Using explicit formulas of geometric sequences

CCSS Math: HSF.IF.A.2, HSF.IF.A.3

## 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.