Question

What are the first four terms in the sequence generated by the formula? an=n^2+2n+1

Answer 1

Given the formula:

$a_n=n^2+2n+1$

First term:

$a_1=1^2+2(1)+1=1+2+1=4$

Second term:

$a_2=2^2+2(2)+1=4+4+1=9$

Third term:

$a_3=3^2+2(3)+1=9+6+1=16$

Fourth term:

$a_4=4^2+2(4)+1=16+8+1=25$

Answer: the first four terms are: 4, 9, 16 and 25