Find the 8th term of the geometric sequence 5, -15, 45, ...5,−15,45,...

Answer 1

5, -15, 45 has common ratio (-3)

A1 =5

A2 = 5(-3) =-15

A3 = -15(-3) = 45

AN = A1(r)^(N-1) = 5(-3)^(N-1)

A8 = 5(-3)^(8-1) = 5(-3)^7 = -5(3)^7 = -5(81)(27) = -10,935

Answer 2

First determine what the common ratio is (it's the number each value is being multiplied by to et the next value). It's clear that the common ration is -3 because 5(-3) = -15 and (-15)(-3) = 45.

The generic equation for a geometric sequence is:

a_n = a₁(r)^n-1

In this case, we found r (r = -3), we also know the first term (a₁ = 5) and we are being asked to find the 8th term so n = 8. That means:

a₈ = 5(-3)^8-1

a₈ = 5(-3)⁷

a₈ = 5(-2187)

a₈ = -10935

It also wouldn't be that hard to just multiply -3 a few times to find the 8th term:

Term Term

No. Value

1 5

2 -15

3 45

4 -135

5 405

6 -1215

7 3645

8 -10935