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Formula for Sum of n Terms of an AP

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Question

Find the sum of first 20 terms of the sequence whose nth term is $a_{n} = A n + B$ .

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Solution

$a_{1}$ = A+B

$a_{20}$ = 20A +B

$S_{20}$ = 20/2(A+B+20A+B)

$S_{20}$ = 10(21A+2B)

$S_{20}$ = 210A+20B

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