Question

If the $10 ^ { t h }$ term of a geometric progression is 9 and $4 ^ { t h }$ term is 4, then its term is.

• A. 6
• B. 36
• C. $\frac { 4 } { 9 }$
• D. $\frac { 9 } { 4 }$

Answer 1

Answer: (A)

6

Answer 2

Accordingly, $a r ^ { 9 } = 9$ and $a r ^ { 3 } = 4$

$\Rightarrow$ $r ^ { 3 } = \frac { 3 } { 2 }$ and $a = \frac { 8 } { 3 }$.

$\therefore$ term i.e. $a r ^ { 6 } = \frac { 8 } { 3 } \left( \frac { 3 } { 2 } \right) ^ { 2 } = 6$.

Trick : term is equidistant from and $4 ^ { t h }$ so it will be $\sqrt { 9 \times 4 } = 6$.