how many terms of the AP 24,21,18,........... must be taken so that their fun is 78
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Let a be the first term and d be the common difference.
Given AP = 21,24,28...
a = 21,d = 21 - 24 = -3,sn = 78.
We know that sum of n terms of an AP sn = n/2(2a + (n - 1) * d)
78 = n/2(2(24) + (n - 1)(-3)
78 = n/2(48 + -3n + 3)
78 = n/2(51 - 3n)
156 = n(51 - 3n)
156 = 51n - 3n^2
3n^2 - 51n + 156 = 0
n^2 - 17n + 52 = 0
n^2 - 13n - 4n + 52 = 0
n(n - 13) - 4(n - 13) = 0
(n - 13)(n - 4) = 0
n = 13 (or) 4.
Therefore the number of terms is either 13 or 4.
Hope this helps!
Given AP = 21,24,28...
a = 21,d = 21 - 24 = -3,sn = 78.
We know that sum of n terms of an AP sn = n/2(2a + (n - 1) * d)
78 = n/2(2(24) + (n - 1)(-3)
78 = n/2(48 + -3n + 3)
78 = n/2(51 - 3n)
156 = n(51 - 3n)
156 = 51n - 3n^2
3n^2 - 51n + 156 = 0
n^2 - 17n + 52 = 0
n^2 - 13n - 4n + 52 = 0
n(n - 13) - 4(n - 13) = 0
(n - 13)(n - 4) = 0
n = 13 (or) 4.
Therefore the number of terms is either 13 or 4.
Hope this helps!
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