Question

The 4th term of a G.P. is 16
and the 7th term is 128. Find
the first term and common
ratio of the series​

Answer 1

$\bf{\underline{Question:-}}$

The 4th term of a G.P. is 16 and the 7th term is 128. Find

the first term and common ratio of the series.

$\bf{\underline{Given:-}}$

• ᵃ4 = 16
• ᵃ7 = 128
• r = ?

$\bf{\underline{Solution:-}}$

$\sf → ar^{4-1}=16$

$\sf → ar^3=16--equ(¡)$

Similarly,

$\sf → ar^{7-1}=128$

$\sf → ar^6 = 128--equ(¡¡)$

By equ(¡) and equ(¡¡)

$\sf\large →\frac{ar^6}{ar^3} =\frac{128}{16}$

$\sf → r^3 = 8$

$\sf → r^3 = \sqrt{8}$

$\sf → r = 2$

$\bf{\underline{Hence:-}}$

• Common ratio of series is 2

Answer 2

Given ,

• The 4th & 7th term of GP are 16 & 128

We know that , the nth term of an GP is given by

$\boxed{ \sf{a_{n} = a {(r)}^{n - 1} }}$

Thus ,

ar^(3) = 16 --- (i)

and

ar^(6) = 128 --- (ii)

Divide eq (ii) by eq (i) , we get

r^(3) = 8

r = 3√8

r = 2

Therefore ,

The common ratio of GP is 2