How many terms of the ap 17 15 13
Asked by admin @ in Math viewed by 275 People
How many terms of the ap 17,15,13,........must be added to get the sum 72? Explain the double answer
Answered by admin @
Heya ...
The common difference of this arithmetic progression is -2, then
:
72 = (n/2) * (2a + (n-1)d), where a is the first term, n is the number of terms and d is the common difference
:
72 = (n/2) * ( (2*17) + (n-1)*(-2) )
:
72 = (n/2) * ( 34 -2n + 2)
:
144 = n * ( 34 -2n + 2)
:
144 = 36n -2n^2
:
2n^2 -36n +144 = 0
:
n^2 -18n +72 = 0
:
(n - 12) * (n - 6) = 0
Hope it helps u...!
#bipasha
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