How many terms of an AP lead to a sum of --- ?
Algebra
Level
2
In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P must be taken for their sum to be equal to 120?
The answer is 8.
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1 solution
For an AP with initial term = "a" and common difference = "d" the sum of the first n terms is equal to
na + d (0 + 1 +2.. n-1) = na + ((n-1) n/2 ) * d
Here a = 1 and d = 4
n + 2*(n)(n-1) = 120
or n + 2 n n - 2n = 120
2 n n - n - 120 = 0
n = ( 1 +/- sqrt(1+960))/4 = (1 +/- 31)/4 n = 8 or -7.5 as n > 0 & integer implies n = 8