Question

Find the sum: 2 + 9 + 16 + ... + 37

Answer 1

Step-by-step explanation:

Sum of arithmetic terms = n/2 × [2a + (n - 1)×d], where 'a' is the first term, 'd' is the common difference between two numbers, and 'n' is the number of terms.

this is the same as n/2 × (a1 + an), because

an = a1 + (n-1)×d

so, for the series above :

a or a1 = 2

d = 7, as every new term is the previous term plus 7.

for n

37 = a1 + (n-1)×d = 2 + (n-1)×7

and now solve for n

35 = 7n - 7

42 = 7n

n = 6

so, the sum of all terms is

6/2 × (2+37) = 3×39 = 117