Question 1063411: How many terms of an AP 17, 15, 13, 11…. must be added to get the sum 72?
Explain the double answer.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 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) )
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72 = (n/2) * ( 34 -2n + 2)
:
144 = n * ( 34 -2n + 2)
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144 = 36n -2n^2
:
2n^2 -36n +144 = 0
:
n^2 -18n +72 = 0
:
(n - 12) * (n - 6) = 0
:
n = 12 or n = 6
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The number of terms can be 12 or 6
:
Inspect the first 12 numbers in the sequence
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17, 15, 13, 11, 9, 7, 5, 3, 1, -1, -3, -5
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Note that 5, 3, 1 and -1, -3, -5 cancel each other in the sum
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