Arithmetic Prog...

If sum of $$n$$ terms of an A.P. is $$3n^2+5n$$ and $$T_m=164 $$, what is the value of m?

There is an auditorium with $$35$$ rows of seats. There are $$20$$ seats in the first row, $$22$$ seats in the second row, $$24$$ seats in the third row, and so on. Find the number of seats in the twenty fifth row.

Which term of the A.P. 5, 12, 19, 26, ............ is 145

$$\displaystyle S =\frac{n}{2}\left [ 2a+\left ( n-1 \right )d \right ]$$; make $$d$$ the subject of formula.

Find the sum of first $$11$$ positive numbers which are multiples of $$6$$.

A man arranges to pay off a debt of Rs. 3600 in 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid he dies leaving one-third of the debt unpaid. Find the value of the first instalment. 

Find the sum of $$A.P.$$ whose first and last term is $$13$$ and $$216$$ respectively & common difference is $$7$$.  

If $$t_{11}$$ and $$t_{16}$$ for an $$A.P.$$ are respectively $$38$$ and $$73$$, then $$t_{31}$$ is $$........$$

In the A.P. 7, 14, 21, ... How many terms are to be considered for getting sum 5740.

The $$n^{th}$$ term of the sequence   $$\displaystyle\frac{1}{p}$$, $$\displaystyle\frac{1 + 2p}{p}$$, $$\displaystyle\frac{1 + 4p}{p}$$,... is