Introduction to Arithmetic Progressions

Find the sum of first $20$ terms of an A.P. whose $n^{th}$ term is given by $T_n=(7-3n)$

The sum of the third and seventh terms of an A.P. is $6$ and their product is $8$. Find the sum of first sixteen terms of the A.P.

If $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ is the A.M. between $a$ and $b$, then find the value of $n$

A manufacturer of laptop produced 6000 units in $3^{rd}$ year and $7000$ units in the $7^{th}$ year. Assuming that production increases uniformly by a fixed number every year, find production in $5^{th}$ year.

Deepak repays his total loan of $₹\mathrm{1,18,000}$ by paying every month starting with the first instalment of $₹1000$. If he increases the instalment by $₹100$ every month. What amount will be paid as the last instalment of loan?

If the $m^{th}$term of an A.P.is $\frac{1}{n}$and $n^{th}$ term is $\frac{1}{m},$then the sum of the first $mn$ terms is

Four numbers are inserted between the numbers $4$ and $39$ such that an A.P. results. Find the biggest of these four numbers.

The ratio of the sum of $m$ and $n$ terms of an A.P. is $m^2:n^2$, then find the ratio of $m^{th}$ and $n^{th}$ term

If $x\ne y$ and the sequences $x,a_1,a_2,y$ and $x,b_1,b_2,y$ each are in A.P., then $\left(\frac{a_2-a_1}{b_2-b_1}\right)$

In an A.P., if the $p^{th}$ term is $\text{'}q\text{'}$ and the $qth$ term is $\text{'}p\text{'}$, then its $n^{th}$ term is

If $9^{th}$ term of an A.P is zero, then its ${29}^{th}$ term is ____ its ${19}^{th}$ term.