Question

How do you find the first five terms of the arithmetic sequence given `a_1=6` and d=-4?

Answer 1

First five terms are `{6,2,-2,-6,-10}`

Explanation:

In an arithmetic sequence, starting from first term as `a_1` and common difference `d`, successive terms are obtained by adding `d` i.e. `a_2=a_1+d`, `a_3=a_2+d`, ........ ,`a_n=a_(n-1)+d`

Hence as `a_1=6` and `d=-4`

`a_2=a_1+d=6+(-4)=6-4=2`

`a_3=a_2+d=2+(-4)=2-4=-2`

`a_4=a_3+d=-2+(-4)=-2-4=-6`

`a_5=a_4+d=-6+(-4)=-6-4=-10`

Hence, first five terms are `{6,2.-2,-6,-10}`