Question

If the $5 ^ { t h }$ term of a G.P. is $\frac { 1 } { 3 }$ and term is $\frac { 16 } { 243 }$, then the term will be.

• A. $\frac { 3 } { 4 }$
• B. $\frac { 1 } { 2 }$
• C. $\frac { 1 } { 3 }$
• D. $\frac { 2 } { 5 }$

Answer 1

Answer: (B)

$\frac { 1 } { 2 }$

Answer 2

$T _ { 5 } = a r ^ { 4 } = \frac { 1 } { 3 }$ …..(i)

and $T _ { 9 } = a r ^ { 8 } = \frac { 16 } { 243 }$ …..(ii)

Solving (i) and (ii), we get $r = \frac { 2 } { 3 }$ and $a = \frac { 27 } { 16 }$

Now term $= a r ^ { 3 } = \frac { 3 ^ { 3 } } { 2 ^ { 4 } } \cdot \frac { 2 ^ { 3 } } { 3 ^ { 3 } } = \frac { 1 } { 2 }$.