What is the average of all numbers between 2000 and 2400 that are divisible by 50?

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Accepted Answer

1. Numbers divisible by 50 from 2000 to 2400 are $2000, 2050, \dots, 2400$.
2. This is an arithmetic sequence with first term $a_1=2000$ and last term $a_n=2400$.
3. The average of an arithmetic sequence is $(a_1+a_n)/2$.
4. So the average = $(2000+2400)/2 = 2200$.

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