Question

The second term of a GP is 27 and 7th term is 1 by 9 find the first term and common ratio

Answer 1

aₙ=arⁿ⁻¹

a₂=27=ar

a₇=1/9=ar⁶

a₂/a₇=27/1/9

243/1=1/r⁵

r⁵=1/243

r=1/3

therefore

a=a₂/r

=27/1/3

=81

Answer 2

The first term is 81.

The common ratio is $\frac{1}{3}$.

Step-by-step explanation:

Given : The second term of a GP is 27 and 7th term is 1 by 9.

To find : The first term and common ratio ?

Solution :

The nth term of G.P is $a_n=ar^{n-1}$

The 2nd term of a GP is 27 i.e. $ar=27$ ...(1)

The 7th term of a GP is $\frac{1}{9}$ i.e. $ar^6=\frac{1}{9}$ ...(2)

Divide (2) by (1),

$\frac{ar^6}{ar}=\frac{\frac{1}{9}}{27}$

$r^5=\frac{1}{243}$

$r^5=\frac{1}{3^5}$

$r^5=(\frac{1}{3})^5$

$r=\frac{1}{3}$

The common ratio is $\frac{1}{3}$.

Substitute in (1),

$a(\frac{1}{3})=27$

$a=27\times 3$

$a=81$

The first term is 81.

#Learn more

The second term of a GP is 2 and the sum of infinite terms in GP is 8 find the first term

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