Question

Find the common ratio the 2nd term is6 and 6th term is 96

Answer 1

Answer:

Common ratio = 2

Step-by-step explanation:

Given---> Second term of GP = 6 and

Sixth term of GP = 96

To find ---> Value of common ratio

Solution---> Let first term and common ratio of GP be 'a' and' r ' respectively

Now formula of nth term of GP is

aₙ = a rⁿ⁻¹

ATQ , second term = 6

a₂ = 6

a r²⁻¹ = 6

a r = 6 ..................... (1)

ATQ , Sixth term = 96

a₆ = 96

a r⁶⁻¹ = 96

a r ⁵ = 96 ..................(2)

Dividing quation (1) by equation (2) we get

a r⁵ / a r = 96 / 6

We have a law of exponent

xᵃ / xᵇ = xᵃ ⁻ᵇ , applying it here

a¹⁻¹ r⁵⁻¹ = 16

a⁰ r⁴ = 2 × 2 × 2 × 2

(1) r⁴ = 2⁴

r = 2

So common ratio is 2

Answer 2

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common ratio =2

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