1 Answer

Xudre · Answer 1 · 2023-12-29T14:36:38+0000

Solution:

Given conditions:

6th term (T6) = -2

first term (a) = 18

n = 6, r = ?

Formula for finding the nth term of a GP:

$tn = a {r}^(n - 1)$

Where:

T = the given value for the number of term(s)

n = the given number of term

a = The first term

r = The common ratio

Replacing for the values:

$- 2 = 18 {r}^(6 - 1) \\ - 2 = 18 {r}^(5)$

Dividing both sides by 18, we have:

${r}^(5) = ( - 2)/(18)$

Now, we have to fifth root both sides to find the value of r.

$\sqrt[5]{ {r}^(5) } = \sqrt[5]{ ( - 2)/(18) }$

Therefore:

Common ratio,
r = -0.0638165752
≈ -0.064 to 3 decimal places.