Question

The first 5 terms of a sequence are shown below:

3, -2, -7, -12, -17
Which expression can be used to find the nth term?

Answer 1

Explanation:

To find the formula for the nth term ,

First , find the common difference or common ratio.

Common difference =

`T_2-T_1 \\ - 2 - 3 \\ = - 5`

Common ratio =

`T_2/T_1 \\ ( - 2)/(3)`

The common difference applies to the other given numbers for example :

`T_3- T_2 = - 7 - ( - 2) \\ = - 7 + 2 = - 5`

this proves that it is an arithmetic sequence and the given formula for the nth term of an arithmetic sequence is

T_n =a(n-1)d

Where n = no of terms

a= first term

d= common difference