SOLUTION: the sum of the first n terms of the arithmetic progression 5,10,15... is 275 .how many terms are there in the sequence?

Question 977391: the sum of the first n terms of the arithmetic progression 5,10,15... is 275 .how many terms are there in the sequence?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Sn = (n * (a1 + an)) / 2
an = a1 + (n - 1) * d
an = 5 + (n - 1) * 5
an = 5n
therefore
275 = (n * (5 + 5n)) / 2
275 = (5n + 5n^2) / 2
550 = 5n + 5n^2
110 = n + n^2
n^2 +n -110 = 0
(n+11)*(n-10) = 0
n = -11 or n = 10
we want the positive n
There are 10 terms in the sequence
check our answer
an = 50 and
275 = (10 * 55) / 2
275 = 275
our answer checks

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