/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 42 Find the sum of the first 80 pos... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Find the sum of the first 80 positive even integers.

Short Answer

Expert verified
The sum of the first 80 positive even numbers is 6480.

Step by step solution

01

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.
02

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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