The sum of multiples of five from 10 to 75, inclusive

Answer 1

Use the formula

Here d = 5 , a1 = 10 and an = 75

an = a1+d(n-1)

so 75 = 10+5(n-1) => 75 = 10+5n-5 => 75 = 5n+5 =>75-5 = 5n

5n=70 and n=70/5 => n= 14

now use the formula

Sn=n/2(a1+an)

Sn=14/2(10+75) =>Sn = 7(85)

Sn = 595

Answer 2

This question is testing you on factoring and grouping. The question is asking you to find the sum of multiples of five from 10 to 75, including 10 and 75, which is basically asking you to find the sum of 10 15 20 ... all the way to 75. If we factor these numbers by 5, you see the question is turning into finding 5*(2+3+4+...+15). You can add them together in your calculator to find the answer.

If you want to find the answer without using a calculator, there is an easier way. There are 14 numerical values within the bracket, and if you observe, you see the first and the last values can add up to 17, the second and the second last values can also add up to 17. Essentially, we will have 7 pairs which all pairs equal to 17. So the sum can be calculated by 17*7. So the answer is 5*7*17, which is 595.

Hope it helps.