# What is the sum of a 36-term arithmetic sequence where the first term is 11 and the last term is 151?

##### 1 Answer

Feb 5, 2016

2916

#### Explanation:

For an arithmetic sequence.

a , a+d , a + 2d , a+3d +........

the nth term = a + (n-1)d

where a is the first and d , the common difference

for n = 36 : 11 + 35d = 151 → 35d =140 → d = 4

the sum to n terms for an arithmetic sequence is :

# S_n = n/2 [ 2a +(n-1)d ]#

#rArr S_36 = 36/2 [ (2xx11) + ( 35 xx 4) ]# = 18 [ 22 +140 ] = 2916