Question

Sequence and Series: Find the sum of all even numbers between 99 and 999.

Answer 1

To find the sum of all even numbers between 99 and 999, we need to find the first even number and the last even number in the sequence.

The first even number greater than or equal to 99 is 100, and the last even number less than or equal to 999 is 998.

Now, we can use the formula for sum of an arithmetic series:

Sn = (n/2)(a1 + an)

where Sn is the sum of the series, n is the number of terms, a1 is the first term, and an is the last term.

In this case, we have:

a1 = 100
an = 998
n = (an - a1)/2 + 1 = (998 - 100)/2 + 1 = 450

Therefore, the sum of all even numbers between 99 and 999 is:

Sn = (450/2)(100 + 998)
= 225(1098)
= 247,950

So, the sum of all even numbers between 99 and 999 is 247,950.