The sum of even numbers between 100, 200 is A) 7650B) 6750 C) 5670

1.	The sum of even numbers between 100, 200 is A) 7650B) 6750 C) 5670 D) 7350
Answer» Correct option is (D) 7350 First & last even numbers between 100 & 200 are 102 & 198 respectively. \(\therefore a_1=a=10^2\;\&\;d=2,a_n=198\) \(\because a_n=a+(n-1)d\) \(\Rightarrow198=102+(n-1)2\) \(\Rightarrow2(n-1)=198-102=96\) \(\Rightarrow n-1=\frac{96}2=48\) \(\Rightarrow n=48+1=49\) \(\therefore\) Sum of even numbers between 100 & 200 is \(S_n=\frac n2[a+a_n]\) \(=\frac{49}2(102+198)\) \(=\frac{49}2\times300\) \(=49\times150=7350\) Correct option is D) 7350

The sum of even numbers between 100, 200 is A) 7650B) 6750 C) 5670 D) 7350

Answer»

Correct option is (D) 7350

First & last even numbers between 100 & 200 are 102 & 198 respectively.

\(\therefore a_1=a=10^2\;\&\;d=2,a_n=198\)

\(\because a_n=a+(n-1)d\)

\(\Rightarrow198=102+(n-1)2\)

\(\Rightarrow2(n-1)=198-102=96\)

\(\Rightarrow n-1=\frac{96}2=48\)

\(\Rightarrow n=48+1=49\)

\(\therefore\) Sum of even numbers between 100 & 200 is

\(S_n=\frac n2[a+a_n]\)

\(=\frac{49}2(102+198)\)

\(=\frac{49}2\times300\)

\(=49\times150=7350\)

Correct option is D) 7350