Problem 42
Question
Find the sum of the first 80 positive even integers.
Step-by-Step Solution
Verified Answer
The sum of the first 80 positive even numbers is 6480.
1Step 1: Find the 80th even number
Using the formula for an arithmetic series term, we plug in the values: \[ term = 2 + (80-1)*2 = 2 + 79*2 = 160 \]. Hence, the 80th even number is 160.
2Step 2: Calculate the sum of the series
Using the formula for sum of an arithmetic series, we plug in the values, where n is 80, the first number is 2 and the last number is 160: \[ sum = 80/2 * (2 + 160) = 40 * 162 = 6480 \].
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