Question

The first 5 terms of a sequence are shown below:

Answer 1

Step-by-step 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 =

$T_2/T_1 \\ \frac{ - 2}{3}$

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