Question

In a G.P. the first, third and fifth terms may be considered as the first, fourth and sixteenth terms of an A.P. Then the fourth term of the A.P., knowing that its first term is 5 is

• A. 10
• B. 12
• C. 16
• D. 20

Answer 1

The correct option is D

20

$a=5,a{r}^2=a+3d,a{r}^4=a+15d$

$\therefore 5r^2=5+3d,5r^4=5+15d$

$\Rightarrow r^4=1+3d$

$\Rightarrow 25r^4=25+75d$

$\Rightarrow (5+3d{)}^2=25+75d$

$\Rightarrow 25+30d+9d^2=25+75d$

$\Rightarrow 9d^2-45d=0$

$\Rightarrow d=50$

$\Rightarrow T_4=a+3d=5+15=20$