SOLUTION: find the mean of all of the numbers from 1 to 1000 that end in 2 a 496 b 497 c 498 d 500

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Question 344995: find the mean of all of the numbers from 1 to 1000 that end in 2
a 496 b 497 c 498 d 500
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
We need to find their sum and the number of terms

The sum is

Sn = 2+12+22+32+42+52+62+72+82+92+102+ ... +972+982+992

This is an arithmetic series with a%5B1%5D=2 and d=10 and a%5Bn%5D=992

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

992+=+2+%2B+%28n-1%2910

992=2%2B10%28n-1%29

992=2%2B10n-10

992=10n-8

1000=10n

100=n

So there are 100 terms:

The sum formula is:

Sn = expr%28n%2F2%29%2A%28a%5B1%5D%2Ba%5Bn%5D%29

S100 = expr%28100%2F2%29%2A%282%2B992%29

S100 = 50%2A%28994%29=49700

So the average term is their sum divided by 100, the number of terms

49700%2F100 = 497.

Edwin