Question

What is the sequence of 2,5,10,17

Answer 1

Given the sequence below

`2,5,10,17`

It follows the rule

`S_n=n^2+1`

Where

`n\text{ is the number of terms}`

Where

`\begin{gathered} n=1 \\ S_n=n^2+1=1^2+1=1+1=2 \end{gathered}`

Where

`\begin{gathered} n=2 \\ S_n=n^2+1=2^2+1=4+1=5 \end{gathered}`

Where

`\begin{gathered} n=3 \\ S_n=n^2+1=3^2+1=9+1=10 \end{gathered}`

Where

`\begin{gathered} n=4 \\ S_n=n^2+1=4^2+1=16+1=17 \end{gathered}`

For the 5th term,

Where

`S_n=n^2+1=5^2+1=25+1=26`

Hence, the sequence is

`S_n=n^2+1`