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The Number Of Terms In AP Is Even,The Sum Of Odd Terms Is 24,Of the even terms is 30. The Last Term Exceeds The First By 10.5 Find the number of terms

The Number Of Terms In AP Is Even,The Sum Of Odd Terms Is 24,Of the even terms is 30. The Last Term Exceeds The First By 10.5 Find the number of terms

Grade:9

1 Answers

Pratik Tibrewal
askIITians Faculty 37 Points
8 years ago
let the A.P. be a, a+d, a+2d, and number of terms be 2n
24 = n/2(2a + (n-1)2d)
=> 24 = n(a+ (n-1)d) ------(1)
30 = n/2(2(a+d) + (n-1)2d)
=> 30 = n(a+d+(n-1)d) ------(2)
also given l - a = 10.5
or a+(2n-1)d - a = 10.5
=> (2n-1)d = 10.5 -----------(3)
from (1): a + (n-1)d = 24/n
put this value in (2)
n(d+24/n) = 30 ----------(4)
substitute the value of d from 3 in 4
n(10.5/(2n-1) + 24/n) = 30
10.5/(2n-1) + 24/n = 30/n
=> 10.5/(2n-1) = 6/n
=> 10.5n = 12n - 6
1.5n = 6
n = 4
Number of terms = 2n = 8




Thanks and Regards,
Pratik Tibrewal
askiitians faculty
BTech

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