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nth Term of A.P

Find the sum ...

Question

Find the sum of first $16$ terms of an A.P. $a_{1}, a_{2}, a_{3}$ ________.

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Solution

$A . P . a_{1}, a_{2}, a_{3} f i r s t t e r m = a_{1} c o m m o n d i f f e r e n c e = a_{2} - a_{1} S_{16} = \frac{16}{2} [2 \times a_{1} (16 - 1) (a_{2} - a_{1})] S_{16} = 8 [2 a_{1} + 15 a_{2} - 15 a_{1}] S_{16} = 8 [15 a_{2} - 13 a_{1}]$

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