Question

Write an explicit formula for the sequence and find the 18th term.
-4, 12, -36...

Answer 1

Nth term = (4/3) × (-3)^n

18th term: 516560652 or 4 × 3¹⁷

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

Answer 2

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

513560652

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