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Question

The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.

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Solution

We know that the nth term of an A.P is given by Tn=a+(n1)d

T4+T8=24 [given]
a+3d+a+7d=24
2a+10d=24.........Eq(1)

And, T6+T10=34 [given]
a+5d+a+9d=34
2a+14d=34............Eq(2)
Subtracting eq.(1) from eq.(2), we have
2a+14d(2a+10d)=3424
4d=10
d=104=52
Put d=52 in eq.(1), we have
2a+10×52=24
2a+25=24
2a=2425
2a=1
a=12


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