Question

Identify the 10th term for the sequence: 12, 6, 3, 3/2...

Answer 1

The geometric sequence 12, 6, 3, 3/2

r = t₂/t₁

r = 6/12 = 1/2

Formula for n^th term in geometric sequence a_n = ar^n-1

^{Where a is first term and r is common ratio.}

To find 10^th term, substitute n = 10, a = 12, r = 1/2 in a_n.

a₁₀ = 12(1/2)^10-1

= 12(1/2⁹)

= 12/512

= 3/128

a₁₀ = 3/128.