Question

Write an expression to describe the sequence below, and then find the 10th term. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

–64, –63, –62, –61, ...

Answer 1

see explanation

Explanation:

there is a common difference between consecutive terms, that is

- 63 - (- 64) = - 63 + 64 = 1

- 62 - (- 63) = - 62 + 63 = 1

- 61 - (- 62) = - 61 + 62 = 1

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = - 64 and d = 1 , then

`a_(n)` = - 64 + 1(n - 1) = - 64 + n - 1 = n - 65

use this rule to find the 10th term

a₁₀ = n - 65 = 10 - 65 = - 55

Answer 2

The sequence can be described using the formula:

`a_(n)` = -64 + (n-1)

∴
`a_(n)` represents the nth term in the sequence.

To find the 10th term, we substitute n = 10 in the above formula:

`a_(10)` = -64 + (10-1) = -64 + 9 = -55

Therefore, the 10th term in the sequence is -55.