Question

Iftar term of a GP is 324 and 7th term is 64 then find 10th term

Answer 1

if the which term??
 say the term

Answer 2

Answer:

10th term of GP is 19

Step-by-step explanation:

Given: 3rd term of GP,  $a_3$ = 324

           7th term of GP,  $a_7$ = 64

To find 10th term of GP, $a_10$

nth term of GP is given by

$a_n=ar^{n-1}$

where a is first term and r is common ratio.

$a_3=324$

$ar^{3-1}=324$

$ar^2=324$ ..................(1)

$a_7=64$

$ar^{7-1}=64$

$ar^6=64$ ..................(2)

Divide (2) by (1)

$\frac{ar^6}{ar^2}=\frac{64}{324}$

$r^4=\frac{64}{324}$

$r^4=\frac{16}{81}$

$r=\pm\frac{2}{3}\:,\:\pm\frac{2}{3}\imath$

$\implies common\:difference=\frac{2}{3}$

put this value in eqn (1).

$a(\frac{2}{3})^2=324$

$a=324\times\frac{9}{4}$

$a=729$

$\implies a_{10}=729\times(\frac{2}{3})^{10-1}=18.962962963$

Therefore, 10th term of GP is 19