Can someone please helppp!! For each sum find: a.) the number of terms, b.) the first term, c.) the last term, and d.) evaluate the sum. Picture below:

Question

anonymous · Answer

$$\sum_{n=1}^{8}\frac{ 2n }{ 3 }$$

anonymous · Answer

ikno there are 8 terms..

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

yes there are 8 terms

jim_thompson5910 · Answer

the first term is 2/3 because this is what you get when you plug in n  =1

jim_thompson5910 · Answer

n = 1 is the first n value you plug in

2n/3 = 2*1/3 = 2/3

So that's why the first term is 2/3

jim_thompson5910 · Answer

the last term is found by plugging in n = 8 (the largest value of n possible)

the sum is found by plugging in n = 1, n = 2, ...., n = 8 and adding up the results

anonymous · Answer

(8/2)[(4/3) + 7(2/3)] = 24 is this the sum?

jim_thompson5910 · Answer

you have an interest way to get there, but yes, the answer is 24

jim_thompson5910 · Answer

interesting*

anonymous · Answer

can you show me how you would do it?

jim_thompson5910 · Answer

well the first term is 2/3

the last term is 2n/3 = 2*8/3 = 16/3

So...

Sn = n*(a1 + an)/2 ... this is the sum of the first n terms in an arithmetic sequence

S8 = 8*(2/3 + 16/3)/2

S8 = 8*(18/3)/2

S8 = 4*(18/3)

S8 = 4*(6)

S8 = 24

anonymous · Answer

Oh okay I see what you did, I like your way better lol thank you!!

jim_thompson5910 · Answer

you're welcome, your way works too, just not sure how you got it