SOLUTION: Find the sum of the arithmetic series with first term 1,common difference 3,and last term hundred

Question 1137789: Find the sum of the arithmetic series with first term 1,common difference 3,and last term hundred
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The sum of the first n terms of an arithmetic sequence is
:
Sum = (n/2) * (2a +d(n-1)), where a is the first term, n is the number of terms to sum, and d is the common difference
:
We are given a=1, d=3
:
We need to determine the nth term of this sequence which is 100
:
The formula for the nth term of an arithmetic sequence is
:
x(n) = x(1) +d(n-1), where x(1) is the first term
:
we are given that the nth term is 100
:
100 = 1 +3(n-1)
:
100 = 1 +3n-3
:
3n = 102
:
n = 34
:
sum = (34/2) * (2(1) +3(34-1))
:
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sum = 17 * (2 +99) = 1717
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