Answer
$a_1 = 3$
$a_2 = 8$
$a_3 = 15$
$a_4 = 24$
$a_5 = 35$
Work Step by Step
Substitute numbers $1$ through $5$ to find the first five terms of this series:
For $n = 1$:
$a_1 = 1^2 + 2(1)$
Evaluate exponents first, according to order of operations:
$a_1 = 1 + 2(1)$
Multiply next:
$a_1 = 1 + 2$
Add to simplify:
$a_1 = 3$
For $n = 2$:
$a_1 = 2^2 + 2(2)$
Evaluate exponents first, according to order of operations:
$a_2 = 4 + 2(2)$
Multiply next:
$a_2 = 4 + 4$
Add to simplify:
$a_2 = 8$
For $n = 3$:
$a_3 = 3^2 + 2(3)$
Evaluate exponents first, according to order of operations:
$a_3 = 9 + 2(3)$
Multiply next:
$a_3 = 9 + 6$
Add to simplify:
$a_3 = 15$
For $n = 4$:
$a_4 = 4^2 + 2(4)$
Evaluate exponents first, according to order of operations:
$a_4 = 16 + 2(4)$
Multiply next:
$a_4 = 16 + 8$
Add to simplify:
$a_4 = 24$
For $n = 5$:
$a_5 = 5^2 + 2(5)$
Evaluate exponents first, according to order of operations:
$a_5 = 25 + 2(5)$
Multiply next:
$a_5 = 25 + 10$
Add to simplify:
$a_5 = 35$
