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Question

Obtain the sum of the 56 term of an A.P. whose 19th and 38th terms are 52 and 128 respectively.

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Solution

Tn=a+(n1)d

Given,

T38=a+37d=128...(1)

T19=a+18d=52...(2)

(1)-(2) gives,

d=4

From (2)

a=5218(4)=20

T56=a+(561)d

=20+55×4

=200

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