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
