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

Solution:

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

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.

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

Summary:

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