Question

This Question: 1 pt Find the sum of the sequence. 47 +48 +49 +50 + ... + 136 The sum is Enter your answer in the answer box.

Answer 1

The sum is
`8235`.

Explanation:

You can use the result that establishes that the sum of the first
`n` natural numbers is given by the formula:

`1+2+3+4+\cdots + (n-1)+ n= (n(n+1))/(2)`.

So, if you have to calculate the sum of the natural numbers from 47 to 136 you can sum from 1 to 136, then subtract the sum from 1 to 46. That is to say,

`47+48+49+50+\cdots+136=(1+2+3+\cdots+46+47+\cdots +136)-(1+2+3+\cdots +46)`.

Using the given formula we have:

`47+48+49+50+\cdots+136=(136\cdot 137)/(2)-(46\cdot 47)/(2)=9316-1081=8235`.