Question

Write an explicit formula for the sequence and find the 18th term.
12, 3, 3/4....

Answer 1

Nth term = 3 × (¼)^(n-2)

18th term: 3/4¹⁶

Explanation:

12 ,3 , ¾..

Are terms of a Geometric progression with:

First term = 12

Common ratio = 3/12 = ¼

Nth term = 12 × (¼)^(n-1)

= (3×4) × (¼)^(n - 2)

= 3 × (¼)^(n-2)

18th term: n = 18

12 × (¼)^(18-1)

12 × (¼)¹⁷

3/4¹⁶ or 6.985 × 10^(-10)

Answer 2

3/4294967296

Explanation:

The common ratio is

3/12 = 1/4

The explicit formula

an = a1 r^(n-1)

an = 12 (1/4)^ (n-1)

The 18th term is

a18 = 12 * (1/4)^17

= 3/4294967296