Question

Find a formula an for the nth term of the arithmetic sequence whose first term is a1=−3 such that an+1−an=4 for n≥1.

Answer 1

Taking into account that $a_{n+1}=a_n+4,$ we conclude that the common difference of an arithmetic sequence is equal to 4. Therefore, the formula for the $n$th term is the following:

$a_n=4(n-1)+a_1=4n-4-3=4n-7.$