Question

In an AP the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 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