Question

Find the sum of odd integers from 1 to 2001​

Answer 1

Solution :

Odd intigers from 1 + 2001 are : 1 , 3 ,5, 7 .......2001

Common difference = 3 - 1 = 2

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀5 -3 = 2

So, Common difference is same which is 2 so, we can say that the given sequence is an AP.

• first term a = 1
• common difference = 2
• an = 2001

an= a + (n - 1)d

2001 = 1 + (n - 1)2

2000/2 = n - 1

1000 + 1 = n

n = 1001

Now,

$\rm \: s_{1001 }= \frac{n}{2} \{2 \times 1 + (1001 - 1) \}2 \\ \\ \rm \: s_{1001 }= \frac{1001}{2} \{2 + 1000 \times 2 \} \\ \\ \rm \: s_{1001 }= \frac{1001}{2} \{2 + 2000 \} \\ \\ \rm \: s_{1001 }= \frac{1001}{2} \times 2002 \\ \\ \rm \: s_{1001 }= 1001 \times 1001 \\ \\ \rm \: s_{1001 }= 1,002,001$

Hence,

• sum of odd intigers from 1 to 2001 is 1002001 .

━━━━━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Done࿐