# Which formula can be used to describe the sequence below –8, –5, –2, 1, 4, ...?

In an arithmetic sequence, the difference between any two consecutive terms is the same throughout the sequence.

## Answer: The formula to describe the sequence –8, –5, –2, 1, 4, ... is 3n - 11.

Let's find the nth term of the sequence.

**Explanation:**

The formula for the nth term can be found using the formula \(a_n\) = [a + (n - 1) d]

In the sequence –8, –5, –2, 1, 4, ...

Given first term = a = \(a_1\) = -8

\(a_2\)_{ }- \(a_1\)_{ }= -5 - (-8) = 3; \(a_3\)_{ }- \(a_2\)_{ }= -2 - (-5) = 3; ...

Since the difference between every two consecutive terms is the same, the given sequence is an arithmetic sequence with d = 3.

⇒ \(a_n\) = [a + (n - 1) d]

⇒ \(a_n\) = [- 8 + (n - 1) 3]

⇒ \(a_n\) = 3n - 11

### Thus, the formula to describe the sequence –8, –5, –2, 1, 4, ... is \(a_n\) = 3n - 11.

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