Find the sum of the series 3+7+14+24+37..

Explanation

`S= 3+7+14+24+37 cdots T_{n}
cdots(1)`


`S= 3+7+14+24 cdots T_{n-1} +T_{n} cdots(2)`


` text { subtracting } (1) - (2) `


` 0=3+(4+7+10+13+T_{n-1}]-T_{n} `


`T_{n} = 3+(frac{n-1}{2})(8+(n-2) times 3)`


`=3+frac{n-1}{2}(3 n+2)`


`=frac{6+3 n^{2}-3 n+2 n-2}{2} `


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