Sum of first 100 odd numbers is A) 10,000 B) 100 C) 1000 D) 1,00,0

1.	Sum of first 100 odd numbers is A) 10,000 B) 100 C) 1000 D) 1,00,000
Answer» Correct option is (A) 10,000 First odd number is 1. We know that two consecutive odd numbers is differ by 2. \(\therefore\) Common difference of arithmetic progression of odd numbers is d = 2. First term of odd numbers is a = 1. \(\therefore\) Sum of first 100 odd numbers is \(S_{100}=\frac{100}2[2a+(100-1)d]\) \((\because S_n=\frac n2[2a+(n-1)d])\) \(=50\,(2\times1+99\times2)\) \((\because a=1\;\&\;d=2)\) \(=50\times2(1+99)\) \(=100\times100=10000\) Hence, sum of first 100 odd numbers is 10000. Correct option is A) 10,000

Sum of first 100 odd numbers is A) 10,000 B) 100 C) 1000 D) 1,00,000

Answer»

Correct option is (A) 10,000

First odd number is 1.

We know that two consecutive odd numbers is differ by 2.

\(\therefore\) Common difference of arithmetic progression of odd numbers is d = 2.

First term of odd numbers is a = 1.

\(\therefore\) Sum of first 100 odd numbers is

\(S_{100}=\frac{100}2[2a+(100-1)d]\) \((\because S_n=\frac n2[2a+(n-1)d])\)

\(=50\,(2\times1+99\times2)\) \((\because a=1\;\&\;d=2)\)

\(=50\times2(1+99)\)

\(=100\times100=10000\)

Hence, sum of first 100 odd numbers is 10000.

Correct option is A) 10,000