Question

the first term of a GP is 64 and the common ratio is "r" if the average of the first and the fourth term is 140 find the value of r and four terms

Answer 1

so r=3/2 and fourth term will be 216

Answer 2

Given:

First term of the GP = a = 64

The common ratio = r

The average of the first and the fourth term = 140

To Find:

The value of r and four terms

Solution:

The nth term of GP = an = $ar^n^-^1$

⇒ a4 = ar³

Given that a + a4 / 2 = 140

Substituting,

$\frac{a+ar^3}{2} = 140$

or a ( 1 + r³) = 280

Substituting a = 64,

1 + r³ = 280 / 64 = 35 / 8

or r³ = 35-8 / 8

= 27 / 8

Taking cube root of both the sides,

r = 3 / 2

The first four terms are as follows:

a = 64

a2 = 64 X 3/2 = 96

a3 = 64 X 9/4 = 144

a4 = 64 X 27 / 8 = 216

Hence, the value of r is 3/2 and the four terms are 64, 96, 144, and 216.