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. -91, -194, -291, -388

Answer 1

`T_n = -97n`

Explanation:

The actual sequence is: -97, -194, -291, -388

Required

Determine the nth term

nth term of an arithmetic progression is:

`T_n = T_1 + (n - 1)d`

Where

`T_1 = First\ Term = -97`

`d = Common\ Difference = -194 - (-97) =-97`

So:

`T_n = T_1 + (n - 1)d` becomes

`T_n = -97 + (n - 1) * -97`

`T_n = -97 -97n + 97`

Collect Like Terms

`T_n = -97n + 97-97`

`T_n = -97n`

Hence, a term of the sequence is:

`T_n = -97n`