# Problem of the Day

What is the sum of all the integers from 90 to 920 that end in 7?

A. 44,094

B. 42,081

C. 41,361

D. 40,147

E. 39,168

### Solution

97+107+117+…+917=

(90+100+110+…+910) + (7+7+7+…7)=

10(9+10+…+91) + (7+7+7+…+7)=

Now, we can use the formula for computing the sum of an arithmetic series. First, note that there are 83 integers from 9 to 91 inclusive. So, multiply the average of 91 and 9, which is 50, with the number of terms, 83, to get 4,150. There would also be 83 7’s in the 2nd part of the sum, so this gives us:

10(4,150)+83(7)=

41500+581=

42,081

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