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

-4, 12, - 36 ...

Nth term = (4/3) * (-3) ^n

18th term: 516560652 or 4 * 3¹⁷

Step-by-step explanation:

-4, 12, - 36 ...

Are terms of a Geometric progression with:

First term = - 4

Common ratio = 12/-4 = - 3

Nth term = - 4 * (-3) ^ (n-1)

= - 4 * (-3) ^ (n) / (-3)

= (-4/-3) * 3^n

= (4/3) * (-3) ^n

18th term: n = 18

-4 * (-3) ^ (18-1)

-4 * (-3) ¹⁷

4 * 3¹⁷

516560652

an = - 4 * (-3) ^ (n-1)

513560652

Step-by-step explanation:

We can find the common ratio

12/-4 = - 3

r = -3

The explicit formula is

an = a1 r^ (n-1)

an = - 4 * (-3) ^ (n-1)

We want the 18 th term

a 18 = - 4 (-3) ^ 17

513560652