Find the sum of the first n terms of the series : `3 + 7 + 13 +21 + 31 +dot dot dot`

Explanation

`S_{n}= 3+7+13+21+ldots+a_{n}`…….(1)


`S_{n}= 3+7+13+ldots+a_{n-1}+ a_{n}` …….(2)


` text { Subtracting (2) from (1) } `


`0=3+(7-3)+(13-7)+(21-3)+cdots +(a_{n}-a_{n-1})-a_{n} `


`a_{n}=3+[4+6+8+cdots(n-1) text { terms }] `


`a=4 quad N=n-1 quad d=2`


a_{n}=3+frac{N}{2}[2 a+(N-1) d]


`a_{n}=3+frac{n-1}{2}[8+2[n-2)]=3+(n-1) {[4+n-2]}`


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