Question

Find the 22nd term of the arithmetic sequence with a1 = -6 and a common difference of d=3

Answer 1

`a_n=a_1+d(n-1) \\ a_1=-6 \\ d=3 \\ a_n=-6+3(n-1)=-6+3n-3=3n-9`

The nth term of the sequence is 3n-9.
Now replace n with 22.


`a_(22)=3 *22-9=66-9=57`

57 is the 22nd term of this sequence.