If the 5 t h term of a G.P. containing positive terms is 1 3 and 9 t h term is 16 243 , then the 4 t h term will be Options: A . &nbsp 3 4 B . &nbsp 1 2 C . &nbsp 1 3 D . &nbsp 2 5

Answer: Option B : B T 5 = a r 4 = 1 3 .......(i) and T 9 = a r 8 = 16 243 .......(ii) Solving (i) and (ii), we get r = 2 3 and a = 27 16 Now 4 t h term = a r 3 = 3 3 2 4 . 2 3 3 3 = 1 2

If the 5th term of a G.P. containing positive terms is 13 and 9th term is 1624

Discussion Forum : Sequences And Series

Question -

If the $5^{t h}$ term of a G.P. containing positive terms is $\frac{1}{3}$ and $9^{t h}$ term is $\frac{16}{243}$ , then the $4^{t h}$ term will be

Options:

A .

\frac{3}{4}

B .

\frac{1}{2}

C .

\frac{1}{3}

D .

\frac{2}{5}

Answer: Option B
:
B

$T_{5}$ = $a r^{4}$ = $\frac{1}{3}$ .......(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 $4^{t h}$ term = $a r^{3}$ = $\frac{3^{3}}{2^{4}} . \frac{2^{3}}{3^{3}}$ = $\frac{1}{2}$

Was this answer helpful ?

Next Question

Discussion Forum : Sequences And Series

Submit Your Solution hear: