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

User Veton
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1 Answer

3 votes

Given the sequence below


2,5,10,17

It follows the rule


S_n=n^2+1

Where


undefined


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

User Tdensmore
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