SOLUTION: The number of terms in an A.P. whose first term is 5, common difference 3, and sum 55 is

Question 1109670: The number of terms in an A.P. whose first term is 5, common difference 3, and sum 55 is
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
the formula for the sum of the first n terms of a arithmetic progression(AP) when we do not know the nth term is
:
s(n) = (n/2) * (2 * a(0) + (n-1) * d), where a(0) is the first term and d is the common difference
:
we are given
:
(1) 55 = (n/2) * (2*5 + 3*(n-1))
:
solve for n
:
55 = (n/2) * (10 + 3n - 3)
:
110 = n * (7 + 3n)
:
3n^2 +7n -110 = 0
:
(3n+22) * (n-5) = 0
:
n = -22/7 and n = 5
:
we reject the negative value for n
:
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there are 5 terms, namely
:
5, 8, 11, 14 , 17
:
to check this we use the formula
:
55 = (5/2) * (2 * 5 + 3 * (5 - 1)
:
55 = (5/2) * 22 = 55
:
our answer checks
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:

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