Question

Find S10 for the series 2 + 7 + 12 + 17 +..
Also explain how to do it please

Answer 1

This is an arithmetic sum follows the formula \(\large \cfrac{n(a_1+a_n)}{2}\)
We've got to find \(a_n\) first. Here, \(\large a_n=a_{10}\) And in order to find \(a_{10}\) we use the formula for arithmetic progression, which is \(\large a_n= a_1+(n-1)d\)

\[\large a_{10}=? \ , \ a_{1} = 2 \ , \ n=10 \ , \ d=5\]\[\large a_{10}= 2+5(10-1)\]\[\large a_{10} = 2+5(9)\]\[\large a_{10} = 47\]
Now that we've found our \(\large a_n\) we can plug it back into our formula for the sum.\[\large S_{10}= \cfrac{10(2+47)}{2}\]\[\large S_{10} = 5(49)\]\[\large S_{10} = ? \]

Answer 2

What did you get as your answer? :)

Answer 3

Sum of an arithmetic series is given by:\[\bf S_n=\frac{n}{2}(2a+(n-1)d)\]Where 'n' is nth term in the sequence, 'a' is the first term, and 'd' is the common difference.

@Jhannybean @Stephachu

Answer 4

So:\[\bf S_{10}=\frac{10}{2}(2(2)+(10-1)5)=?\]@Stephachu @Jhannybean Evaluate.

Answer 5

I think my way works perfectly fine, we're getting the same outcome as well.

Answer 6

s10 = 5(4+5(9)) = Same outcome as mine, lol.

Mine is just broken up into steps to explain how to get the arithmetic series for 10 numbers, and then finding the sum using the arithmetic series. :)

Answer 7

I got 245?

Answer 8

good job.

Answer 9

Thank you!^^

Answer 10

Np : D