Question

Use the arithmetic progression formula to find the sum of integers from 75 to 100.75,76,77....99,100.​

Answer 1

The sum is 2275

Explanation:

Given

`75,76,77....99,100`

Required

The sum

Using arithmetic progression, we have:

`S_n = (n)/(2)(T_1 + T_n)`

Where:

`T_1 = 75` --- first term

`T_n = 100` --- last term

`n = T_n - T_1 + 1`

`n = 100 - 75 + 1 = 26`

So, we have:

`S_n = (n)/(2)(T_1 + T_n)`

`S_n = (26)/(2)*(75 + 100)`

`S_n = 13*175`

`S_n = 2275`