Question

Sum of natural numbers between 100 and 150.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Sum of natural numbers between 100 and 150 = 6125

Given :

The natural numbers between 100 and 150

To find :

Sum of natural numbers between 100 and 150

Formula :

Sum of first n terms of an arithmetic progression

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

Where First term = a

Common Difference = d

Solution :

Step 1 of 3 :

Write down all natural numbers between 100 and 150

All natural numbers between 100 and 150 are 101 , 102 , 103 , 104 , . . . . , 149

This is an arithmetic progression

Step 2 of 3 :

Calculate number of terms

First term = a = 101

Common Difference = d = 102 - 101 = 1

Let there are n terms in the arithmetic progression

Then nth term of the AP = 149

a + (n - 1)d = 149

⇒ 101 + (n - 1) × 1 = 149

⇒ 101 + n - 1 = 149

⇒ n + 100 = 149

⇒ n = 149 - 100

⇒ n = 49

Step 3 of 3 :

Calculate sum of natural numbers between 100 and 150

Number of terms = n = 49

∴ The sum of all odd numbers from 1 to 41

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

$\displaystyle \sf = \frac{49}{2} \bigg[(2 \times 101) + (49 - 1) \times 1 \bigg]$

$\displaystyle \sf = \frac{49}{2} \times \bigg[202 + 48 \bigg]$

$\displaystyle \sf = \frac{49}{2} \times 250 \bigg]$

$\displaystyle \sf = 49 \times 125$

$\displaystyle \sf = 6125$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If the middle term of a finite AP with 7 terms is 21 find the sum of all terms of the AP

https://brainly.in/question/30198388

2. find the 100th term of an AP whose nth term is 3n+1

https://brainly.in/question/22293445

#SPJ3