Write the rule for the nth term of the geometric sequence. Then find a5

a2 = 20, r = 1/4

aₙ = a₁rⁿ⁻¹

a₅ = 5/16

Step-by-step explanation:

Formula:

nth term of geometric sequence

aₙ = a₁rⁿ⁻¹

aₙ - nth term

a₁ - first term

r - common ratio

To find a₅

It is given that, a2 = 20, r = 1/4

we can find a₁

a₁ = a₂/r = 20 / (1/4) = 20 * 4 = 80

aₙ = a₁rⁿ⁻¹

a₅ = a₁r⁽⁵⁻¹⁾ = 80 * (1/4) ⁴ = 5/16

Therefore a₅ = 5/16

Rule for nth term is:aₙ = a₁rⁿ⁻¹ and value of a5 term is: 5/16

Explanation:

As formula for nth term of geometric sequence is aₙ = a₁rⁿ⁻¹

So aₙ is nth term and a₁ is first term and r is common ratio between any two terms.

we already given that, a2 = 20, r = 1/4

So we can find value of a₁

a₁ = a₂/r = 20 / (1/4) = 20 * 4 = 80

by using formula of nth term of gemometric sequence

aₙ = a₁rⁿ⁻¹

a₅ = a₁r⁽⁵⁻¹⁾ = 80 * (1/4) ⁴ = 5/16

value of a₅ = 5/16