Question

Q.17 

Answer 1

(1) Odd number netween 50 and 150 are as follows : 

` 51,53,55,.........149` 

This forms as A.P. with first term a =581, common difference d=2 and last term L=149

Let there be a terms in this A.P

Then , `I= t_n=149`

`⇒ a+(n-1)d=149`

`⇒51+(n-1)xx2=149`

`⇒(n-1)xx2=98`

`⇒n-1=49`

`⇒n=50`

`∴ "Required sum "=501/2(51+149)=25xx200=5000` 

(2) Even numbers between 100 and 200 are as follows: 

`102,104,106,................198`

This forms as A.P. with first term a = 102, common difference=2 and last term I =198 

Let there be n terms in this A.P

Then,`I=t_n=198`

`⇒ a+(n-1)d=198`

`⇒102+(n-1)xx2=198`

`⇒(n-1)xx2=96`

`⇒ n-1=48`

`⇒n=49`

`∴ "Required sum" =49/2(102+198)=49/2xx300=7350`