If $x+1, 3x$ and $4x+2$ are three consecutive terms of an $A.P.$,find the value of $x$.

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

The first four terms of an $AP,$ whose first term is $-2$ and the common difference is $-2,$ are

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.

$1^{2}, 5^{2}, 7^{2}, 73, \ldots$ are $APs$? If they form an $AP,$ find the common difference $d$ and write three more terms.

Are $1, 3, 9, 27, \ldots$ in $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.