The fifth term of an A.P. is thrice the second term and the twelfth term exceeds twice the $6\mathrm{th}$ term by $1$. Find the $16\mathrm{th}$term.

The sum of the $4\mathrm{th}$ and $8\mathrm{th}$terms of an A.P. is $24$ and the sum of the $6\mathrm{th}$and $10\mathrm{th}$term is $34$. Find the first four tems of the A.P.

If $\left(p+1\right)th$ term of an A.P. is twice the $\left(q+1\right)th$ term, prove that the $\left(3p+1\right)th$ term is twice the $\left(p+q+1\right)th$ term.

In an A.P., if  the $mth$ term is $n$ and $nth$ term is $m$, show that $rth$ term is $(m+n-r)$.

In a certain A.P., the $32\mathrm{nd}$term is twice the $12\mathrm{th}$term. Prove that $70\mathrm{th}$term is twice the $31\mathrm{st}$term.

Two A.P.s have the same common difference.The first term of one these is $3$, and that of the other is $8$. What is the difference between their $2nd$ terms?

Two A.P.s have the same common difference.The first term of one these is $3$, and that of the other is $8$. What is the difference between their $4th$ terms?

Two A.P.s have the same common difference. The first term of one these is $3$, and that of the other is $8$. What is the difference between their $10th$ terms?

Two A.P.s have the same common difference.The first term of one these is $3$, and that of the other is $8$. What is the difference between their $30th$ terms?