Question

Given a term in a geometric sequence and the common ratio. Find the explicit formula . A) a 3 =-36 , r = 6 b) a 6 =64 , r = 2

Answer 1

Explanation:

The explicit formula for a GP is expressed as

Tn = ar^{n-1}

a is the first term

n is the number of terms

r is the common ratio

a) If a3 = 36 and r = 6

a3 = ar^3-1

a3 = ar^2 = 36

ar^2 = 36

a(6)^2 = 36

36a = 36

a = 1

Get the nth term

Tn = 1(6)^{n-1}

Tn = 6^{n-1}

b) If a6 = 64 and r = 2

a6 = ar^6-1

a6 = ar^5 = 64

ar^5 = 64

a(2)^2 = 64

4a = 64

a = 16

Get the nth term

Tn = 16(2)^{n-1}

Tn = 16*(2^n/2)

Tn = 8(2^n)