In the set of positive integers from 1 to 500, what is the sum of all the odd multiples of 5?
A. 10,000
B. 12,500
C. 17,500
D. 22,500
E. 25,000
[spoiler]OA=B[/spoiler]
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In the set of positive integers from 1 to 500, what is the sum of all the odd multiples of 5?
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deloitte247
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Odd multiples of 5 are in the sequence:
5, 15, 25, 35..........n with a common difference of 10
There are 500/5 = 100 multiples of 5 from 1 to 500 in which half are odd and half are even. Hence there are 50 odd multiples from 1 to 500
Therefore, the sequence of odd multiples of 5 from 1 to 500 =>
5, 15, 25, 35, 45, 55..................495
Where d = 10, a = 5, l = 495, and n = 50
$$Sum\ of\ all\ the\ 50\ terms\ =\frac{n\left(a+l\right)}{2}$$
$$=\frac{50\left(5+495\right)}{2}=25\cdot500$$
$$=12,500$$
Answer = B
5, 15, 25, 35..........n with a common difference of 10
There are 500/5 = 100 multiples of 5 from 1 to 500 in which half are odd and half are even. Hence there are 50 odd multiples from 1 to 500
Therefore, the sequence of odd multiples of 5 from 1 to 500 =>
5, 15, 25, 35, 45, 55..................495
Where d = 10, a = 5, l = 495, and n = 50
$$Sum\ of\ all\ the\ 50\ terms\ =\frac{n\left(a+l\right)}{2}$$
$$=\frac{50\left(5+495\right)}{2}=25\cdot500$$
$$=12,500$$
Answer = B
