Question

Sums of first five and twenty-one terms of an A.P are respectively 320 and -168 . Find the first term , common difference , sum of 12 term and 10 term of the series

Answer 1

Given ;

S5 = 320
S21 = -168

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

S5 = (5/2) [2a+4d)
320 = 5(a+2d)
a+2d = 54
a = 54-2d

S21 = (21/2) [2a+20d)
-168 = 21(a+10d)
a+10d = -8
a = -8-10d

54-2d = -8-10d
54+8 = 2d-10d
31 = -4d
d = (-31/4)

a = 54-2d
a = 54+(31/2)
a = 139/2
---------------–----------------