Question

HOTS: In an AP the first term is 2 and the sum of the first 5 terms is 1/4 of the sum of the of the next 5 terms. Show that the 20th term is -112

Answer 1

Let a be the first term. Then a =2.

sum of first 5 terms S5 = 5/2[2+2+(5-1)d]
= 10+10d


Sum of first 10 terms S10 = 10/2[2+2+(10-1)d]
= 20+45d

For calculation of sum of next five terms is S10-S5 = 10+35d


sum of first five terms = ¼ sum of next 5

10+10d = 1/4[ 10+ 35d]
40+40d=10+35d
5d=-30
on simplification d=-6

a20 = a+19d
= 2+(19*-6)
= 2-114
= -112