Question

If $x , 2 x + 2,3 x + 3$are in G.P., then the fourth term is.

• A. 27
• B. $- 27$
• C. 13.5
• D. $- 13.5$

Answer 1

Answer: (D)

$- 13.5$

Answer 2

Given that $x , 2 x + 2,3 x + 3$ are in G.P.

Therefore, $( 2 x + 2 ) ^ { 2 } = x ( 3 x + 3 ) \Rightarrow x ^ { 2 } + 5 x + 4 = 0$

$\Rightarrow ( x + 4 ) ( x + 1 ) = 0 \Rightarrow x = - 1 , - 4$

Now first term $a = x$

Second term $a r = 2 ( x + 1 )$ $\Rightarrow r = \frac { 2 ( x + 1 ) } { x }$

then term $= a r ^ { 3 }$ $= x \left[ \frac { 2 ( x + 1 ) } { x } \right] ^ { 3 } = \frac { 8 } { x ^ { 2 } } ( x + 1 ) ^ { 3 }$

Putting $x = - 4$

We get $T _ { 4 } = \frac { 8 } { 16 } ( - 3 ) ^ { 3 } = - \frac { 27 } { 2 } = - 13.5$ .