SOLUTION: Determine the sum of all the two-digit multiples of 5.

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Question 1181281: Determine the sum of all the two-digit multiples of 5.

Found 3 solutions by josgarithmetic, ikleyn, math_helper:
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website!
10+15+20+25+,...+95

from n 1 to 17;
and use a formula if you want.

Answer by ikleyn(52890)   (Show Source):
You can put this solution on YOUR website!
.
Determine the sum of all the two-digit multiples of 5
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This sum is S = 10 + 15 + 20 + 25 + . . . + 95. (1) Let's consider instead the sum T = 5 + 10 + 15 + 20 + 25 + . . . + 95. (2) The sum (2) is equal to T = 5*(1 + 2 + 3 + 4 + 5 + . . . + 19) It is well known fact that 1 + 2 + 3 + 4 + 5 + . . . + 19 = = 19*10 = 190. (the sum of the first n natural numbers). So, T = 5*190 = 950; hence, S = T - 5 = 950-5 = 945 and can be computed mentally. ANSWER. The sum of all the two-digit multiples of 5 is 945.

Solved.

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    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

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Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website!

The sequence {10, 15, 20, ..., 95} is an AP with , , and common difference (but we don't need d to solve this problem):
Sum = S =