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nth Term of A.P

Sum of n te...

Question

Sum of $n$ terms of $A$ is $n^{2} + 2 n .$ Find the first term and common difference

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Solution

Given,

$S_{n} = n^{2} + 2 n$

first term,

$S_{1} = a_{1} = 1^{2} + 2 (1) = 3$

$S_{2} = a_{1} + a_{2} = 2^{2} + 2 (2) = 8$

common difference

$d = a_{2} - a_{1} = (8 - 3) - 3 = 2$

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