(i) The fee charged from a student every month by a school for the whole session is
` 400, 400, 400, 400, …`
Which form an AP, with common difference (d) `=400-400=0`
(ii) The fee charged month by a school from I to XII is
`250,(250+50),(250+2xx50),(250+3xx50), ...`
i.e, `250,300,350,400, ...`
which form an AP, with common difference (d) `=300-250=50`
(iii) Simple interest `=("Principal" xx "Rate" xx "Time")/(100)`
` " " =(1000xx10xx1)/(100)=100`
So, the amount of money in the account of Varun at the end of every year is
`1000,(1000+100xx1),(1000+100xx2),(1000+100xx3), ...`
i.e., `1000,1100,1200,1300, ...`
which form an AP, with common difference (d) `=1100-1000=100`
(iv) Let the number of bacteria in a certain food `= x`
Since, they double in every sceond.
` :. x,2x,2(2x),2(2*2*x), ...`
i.e., `x,2x,4x,8x, ...`
Now, let ` " " t_(1)=x,t_(2)=2x,t_(3)=4x` and `t_(4)=8x`
`t_(2)-t_(1)=2x-x=x`
`t_(3)-t_(2)=4x-2x=2x`
`t_(4)-t_(3)=8x-4x=4x`
Since, the difference between each successive term is not same. So, the list does form an AP.