The $20^{th}$ term of the $A.P.$ $1, 11, 21, \ldots$ is........

Divya deposited $Rs. 1000$ at compound interest at the rate of $10\%$ per annum. The amounts at the end of the first year,second year,third year,$\ldots,$ form an $AP$. Justify your answer.

Verify that each of the following is an $AP$,and then write its next three terms.
$a, 2a+1, 3a+2, 4a+3, \ldots$

Determine $k$ so that $k^{2}+4k+8, 2k^{2}+3k+6, 3k^{2}+4k+4$ are three consecutive terms of an $AP$.

Yasmeen saves $Rs.\, 32$ during the first month,$Rs.\, 36$ in the second month,and $Rs.\, 40$ in the third month. If she continues to save in this manner,in how many months will she save $Rs.\, 2000$?

In an $A.P.$,ten times the $10^{th}$ term equals fifteen times the $15^{th}$ term. Prove that the $25^{th}$ term of the $A.P.$ is $0$.