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Question

In an A.P of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. find the A.P

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Solution

Given,
n=50
Sn=n2[2a+(n1)d]
S10=102[2a+(101)d]=210
2a+9d=42.....(1)

15th term from last =5015+1=36th term
a36=a+35d

sum of last 15 terms,

152[2a36+(151)d]=2565
152[2(a+35d)+14d]=2565
a+42d=171.......(2)

From (1) and (2), we get,
d=4,a=3

Therefore the series is,
3,7,11,15,............,199

Hence, this is the answer.

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