Question

The seventh term of a GP is 4 times the 5th term. What will be the first term when its 4th term is 40?

Answer 1

EXPLANATION.

• GIVEN

7th term of an Gp is 4 times the 5th term.

What will be the first term when it's 4th term

is 40.

According to the question,

Nth term of an Gp

$\bold{= > \: \: t_{n} \: = ar {}^{(n \: - \: 1)} }$

Case = 1

=> 7th term = 4 ( 5th term)

$\bold{= > \: \: ar {}^{6} = 4(ar {}^{4} )}$

=> r² = 4

=> r = 2

Case = 2

What will be the first term when it's 4th term

is 40.

=> 4th term = 40

=> ar³ = 40

put the value of r = 2 in equation

=> a(2)³ =40

=> 8a = 40

=> a = 5

Therefore,

value of first term = a = 5

value of common difference = r = 2