Write an explicit formula for the sequence and find the 18th term.

12, 3, 3/4 ...

Nth term = 3 * (¼) ^ (n-2)

18th term: 3/4¹⁶

Step-by-step 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)

3/4294967296

Step-by-step 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