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## Algebra (all content)

### Course: Algebra (all content)>Unit 18

Lesson 2: Arithmetic series

# Worked example: arithmetic series (sum expression)

Sal evaluates the arithmetic sum (-50)+(-44)+(-38)+...+2044. He does that by finding the number of terms and using the arithmetic series formula (a₁+aₙ)*n/2.

## Want to join the conversation?

• At , Sal says "-50 + 2044 is equal to 2094"; however, when I added 2044 to -50 by hand and on a calculator the answer I got was that -50 + 2044 = 1994. Did I make a mistake in my math?
• at Sal corrects his mistake by saying, "my brain really wasn't working a while ago"
• I got n to be 348. Did I make a mistake in my algebra?
• You may have subtracted 1 instead of adding 1 in the last step.
The nth term of an arithmetic series is given by a_n = a + d(n - 1), where a is the first term and d is the common difference.
We know that a = -50, d = 6, and a_n = 2,044.
So 2,044 = -50 + 6(n - 1); 2,094 = 6(n - 1); 349 = n - 1; n = 350.
• Wouldn't it be easier to 0 index all these series instead of 1 indexing them? That way we don't need to put k-1 but can instead put k?
• That's what I did as well. I don't think it makes any difference, but it is important to note that if you do it this way, then your Summation will go from k=0 to 349 instead of k=1 to 350.
• I'm very confuzzled on this can someone like explain it better?
• Could you please specify at what time in the video, so that I don't have to watch the full video to figure out where would be your question regard to.
• Instead of using Sal's method to get 350 terms, I found the formula next to the sigma symbol, which was 6k - 56. Then, I put this equal to 2044 and I also got 350 terms. Is this also a viable method, or did I just get lucky?
• That would also be a working method to find out how many terms there are. What you essentially did was find the explicit formula for the sequence and used that to find the term at which the sequence would equal 2044.
• can I use this formula for
3 + 16 + 29 +42...+2044

I figured n=158. My answer was 161,713. Is this correct?
• As long as it is an arithmetic sequence, it is okay to use the formula.
• Why-did-he-divide-350-by-2
• because part of the formula is to divide the sum of the 1st term + the last term by 2