Question

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

Answer 1

Answer:

The sum is 2275

Step-by-step explanation:

Given

$75,76,77....99,100$

Required

The sum

Using arithmetic progression, we have:

$S_n = \frac{n}{2}(T_1 + T_n)$

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:

$S_n = \frac{n}{2}(T_1 + T_n)$

$S_n = \frac{26}{2}*(75 + 100)$

$S_n = 13*175$

$S_n = 2275$