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the num of terms in an AAAP is even;the sum of odd terms is 24,of the even terms is 30,and the last term exceeds the first term by 21/2,find the num of terms and the series

the num of terms in an AAAP is even;the sum of odd terms is 24,of the even terms is 30,and the last term exceeds the first term by 21/2,find the num of terms and the series

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question
Let the total number of terms=2n
According to the question
T1+T3+.......+T2n-1=24.......(1)
T2+T4+...........+T2n=30.........(2)
subtracting 2 from 1 we get
(d+d+d+....)=6
so nd=6
T2n=T1+21/2
T2n-a=21/2
a+(2n-1)d-a=21/2
2nd-d=21/2
2(6)-d=21/2
So d=3/2
nd=6 so n=4
2n=8
So number of terms=8
T2+T4+...........+T2n=30
(a+d)+(a+3d)+....+(a+(2n-1)d)=30
by putting n=4,a=3/2 we get d=3/2
So,the series will be 3/2,3,9/2,......

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