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Question

The number of terms in an A.P. is even; the sum of the odd terms is 24, of the even terms 30, and the last term exceeds the first by 1012 : find the number of terms.

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Solution

Let the total numbers of terms be 2n

According to question:
T1+T3+T5+...+T2n1=24(I)

T2+T4+T6+...+T2n=30(II)

Subtract (I) from (II)

(d+d+...)=6

nd=6

T2n=T1+212

T2na=212

a+(2n1)da=212

2ndd=212

2×6d=212

[d=32]

nd=6
n×32=6
n=4
Total number of terms =2n=2×4=8

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