Question

What is the sum of the arithmetic sequence 3, 9, 15..., if there are 26 terms?

Answer 1

9 - 3 = 6, 15-9 = 6 the difference is 6, So d = 6

First term: a1 = 3


Sn = n*(a1 + an)/2

Sn = n*(a1 + a1 + (n-1)*d)/2

Sn = n*(2*a1 + (n-1)*d)/2

 substitute 26 for n
S26 = 26*(2*a1 + (26-1)*d)/2

substitute 3 for a1

S26 = 26*(2*3 + (26-1)*d)/2

substitute 6 for d

S26 = 26*(2*3 + (26-1)*6)/2  

S26 = 2,028

Answer 2

Sum of an arithmetic series is:

S = n*(a_1+a_n)/2, that easy.

n is the number of terms, 26 in your case. a_n is a_26. We need to find the series!

a_n = a_1 + (n-1)*d, the difference, d, is 6.

So a_n = 3 + (n-1)*6 = 6*n-3 (check it works: 3, 9, 15, ...)

Now a_26 = 6*26-3 = 153, so finally:

S = 26*(3+153)/2 = 26*78 = 2028

2028 is the answer