Question

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

–77, –76, –75, –74, ...

Answer 1

`a_n=n-78`

Explanation:

Given sequence:

-77, -76, -75, -74, ...

This is an arithmetic sequence as the difference between each term is the same.

General form of an arithmetic sequence

`\boxed{a_n=a+(n-1)d}`

Where:

• 
  `a_n` is the nth term.
• 
  `a` is the first term.
• 
  `d` is the common difference between terms.
• 
  `n` is the position of the term.

To find the common difference (d), subtract consecutive terms:

`\implies d=a_2-a_1=-76-(-77)=1`

Substitute the first term and the found common difference into the formula to create an equation for the nth term:

`\implies a_n=-77+(n-1)(1)`

`\implies a_n=-77+(n-1)`

`\implies a_n=-77+n-1`

`\implies a_n=n-78`