Question

The sum of first 100 multiples of 5

Answer 1

Step-by-step explanation:

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Answer 2

The sum of first 100 multiples of 5 is 25250

Given :

First 100 multiples of 5

To find :

The sum of first 100 multiples of 5

Formula :

Sum of first n terms of an arithmetic progression is given by ,

$\displaystyle \sf S_n= \frac{n}{2} \bigg[2a + (n - 1)d \bigg]$

Where First term = a

Common Difference = d

Solution :

Step 1 of 3 :

Write down the first 100 multiples of 5

First 100 multiples of 5 are 5 , 10 , 15 , 20 , . . . . , 500

This is an arithmetic progression

Step 2 of 3 :

Write down first term and common difference

First term = a = 5

Common Difference = d = 10 - 5 = 5

Step 3 of 3 :

Calculate sum of first 100 multiples of 5

Number of terms = n = 100

∴ The sum of first 100 multiples of 5

$\displaystyle \sf = \frac{n}{2} \bigg[2a + (n - 1)d \bigg]$

$\displaystyle \sf = \frac{100}{2} \bigg[(2 \times 5) + (100 - 1) \times 5 \bigg]$

$\displaystyle \sf = 50 \times \bigg[10 + (99 \times 5) \bigg]$

$\displaystyle \sf = 50 \times \bigg[10 + 495 \bigg]$

$\displaystyle \sf = 50 \times 505$

$\displaystyle \sf = 25250$

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