Find the Third Term in the Sequence n²+1: Step-by-Step Solution

To solve this problem, we'll follow these steps:

• Step 1: Use the formula $n^2 + 1$ to find the first element when $n = 1$.
• Step 2: Use the formula $n^2 + 1$ to find the second element when $n = 2$.
• Step 3: Use the formula $n^2 + 1$ to find the third element when $n = 3$.

Let's work through each step:

Step 1: For the first element, substitute $n = 1$ into the formula:
$1^2 + 1 = 1 + 1 = 2$.

Step 2: For the second element, substitute $n = 2$ into the formula:
$2^2 + 1 = 4 + 1 = 5$.

Step 3: For the third element, substitute $n = 3$ into the formula:
$3^2 + 1 = 9 + 1 = 10$.

Therefore, the third element of the series is 10.