# Find the average of all multiples pf 7 between 7 and 777, inclusive?

please show and explain work thanks

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Lv 4
10 years ago

392.

you add up all the multiples, then divide by the number of multiples.

• 10 years ago

if the question was find the average of the multiples of 7 from 7 to 77 inclusive, we would have

(7 + 14 + 21 + 28 + 35 + 42 +49 + 56 + 63 + 70 + 77) / the number of multiples of 7 = 462/11 = 42

note that the 6th, or middle number of the string is 42

we could also take out a factor of 7 and have 7( sum of 1 to 11) = 7(11)(12) / 2 = 7(132)/2 = 7(66) = 462

so for your question, the average is 392, which is the 56th or middle number of that string of numbers.

note that the sum of a string of numbers from 1 to whatever is given by the formula :- S = (n)(n+1) / 2

where n is the last number in the string. so the sum of the first 11 numbers is (11)(12) / 2

and the sum of the numbers 7 to 777 = 7[ (111)(112)] / 2 = 7(111)(56) =43512

so the average is 43512 / 111 = 392