Question

If 3rd term of a gp is 324 and 7th term is 64 then find 10th term

Answer 1

the 10th term of given AP is 512/27

Answer 2

Answer:

10th term of GP is 18.96

Step-by-step explanation:

We are given that 3rd term of GP = 324 , 7th term of GP = 64

We have to find 10th term of G

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 18.96