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Question

How many terms of the series 54,51,48,... be taken so that their sum is 513? Explain the answer.

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Solution

a=54

d=3

Sn=513

Sn=n2(2a+(n1)d)

513=n2(108+33n)

1026=111n3n2

n237n+342=0

(n18)(n19)=0

on solving, we get

n=18,n=19

We are getting here 2 values, on checking we can conclude that as the 19th term is 0 so adding it in the series doesn't make a difference.


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