The first term of a geometric sequence is 9 and the common ratio is -1 over 3. find the fourth term

use your definitions

fourth term = ar^3
= 9(-1/3)^3
= 9(-1/27)
= -1/3

or
simply list the first 4 terms to see the 4th term

9, -3, 1, -1/3, ...

To find the fourth term of a geometric sequence, we need to use the formula:

nth term = a * r^(n-1)

Where:
- nth term is the term we want to find
- a is the first term of the sequence
- r is the common ratio
- n is the term number

In this case, the first term (a) is 9, the common ratio (r) is -1/3, and we want to find the fourth term (n = 4).

Plugging in the values, we get:

4th term = 9 * (-1/3)^(4-1)

Simplifying:

4th term = 9 * (-1/3)^3

Calculating:

4th term = 9 * (-1/27)

Simplifying:

4th term = -9/27

Final calculation:

4th term = -1/3

To find the fourth term of a geometric sequence, we can use the formula:

𝑎ₙ = 𝑎₁ × 𝑟^(𝑛-1)

where:
𝑎ₙ = the 𝑛-th term of the sequence
𝑎₁ = the first term of the sequence
𝑟 = the common ratio of the sequence
𝑛 = the position of the term in the sequence

Given that the first term is 9 and the common ratio is -1/3, we can substitute these values into the formula and solve for the fourth term:

𝑎₄ = 9 × (-1/3)^(4-1)
= 9 × (-1/3)^3
= 9 × (-1/27)
= -9/27
= -1/3

Therefore, the fourth term of the geometric sequence is -1/3.