Question

In an A.P. of which 1 is the first term, if the second, tenth and thirty fourth terms form a G.P. then the fourth term of the A.P. is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$T_2,T_{10},T_{34}$ are in G.P. i.e., 1 + d, 1 + 9d, 1 + 33d are in G.P. $(1+9d{)}^2=(1+d\left)\right(1+33d)\Rightarrow (3d-1)d=0\Rightarrow d=\frac{1}{3},T_4=1+3d=1+1=2$