Question

Find the sum of the following AP's.
(i) -37, -33, -29, .... to 12 terms
(ii) 115,112,110, ... to 11 terms.

Answer 1

(i) -37, -33, -29 ... to 12 terms

First term = a = -37

Common difference = d = -33 - (-37) = 4

n = 12

Applying formula, $S_n$=$\frac{n}{2}$(2a+ (n−1) d) to find sum of n terms of AP, we get

$S_n$=$\frac{12}{2}$[−74+ (12−1) (4)] =6[−74+44] =6[−30] =−180

(ii) 115,112,110... to 11 terms

First tern = a = 115

Common difference = d = 112−115= -3

Applying formula, $S_n$=$\frac{n}{2}$(2a+ (n−1) d) to find sum of n terms of AP, we get

$S_n$=$\frac{11}{2}$[2(115)+ (11−1) (-3)] =$\frac{11}{2}$[230 - 30] =11/2[200]= 1100