Find the sum of all even numbers from 1 to 350.

To find the sum of all even numbers from 1 to 350, we can use the formula for the sum of an arithmetic progression (AP):

Step 1: Identify the sequence
The even numbers between 1 and 350 are: 2, 4, 6, ..., 350.

This sequence is an arithmetic progression where:

First term (a) = 2
Common difference (d) = 2
Last term (l) = 350
Step 2: Find the number of terms in the sequence
The formula to find the number of terms (n) in an AP is: n = (l - a) / d + 1

Substitute the values: n = (350 - 2) / 2 + 1 n = 348 / 2 + 1 n = 174 + 1 n = 175

So, there are 175 terms in the sequence.

Step 3: Use the formula for the sum of an AP
The sum of an AP is given by: S = n/2 * (a + l)

Substitute the values: S = 175/2 * (2 + 350) S = 175/2 * 352 S = 175 * 176 S = 30800

Final Answer:
The sum of all even numbers from 1 to 350 is 30800.