Arithmetic Progressions

Find the 25th term of the AP: $2, 4.5, 7, 9.5, ...$

Which term of the AP $72, 63, 54, ...$ is $0$?

If the first term of an AP is $-2$ and the common difference is $-2$, find the 5th term.

What is the common difference of an AP whose $n$th term is $a_n = 6n + 2$?

A manufacturer of solar panels produced $800$ units in the $4^{th}$ year and $1100$ units in the $9^{th}$ year. Assuming the production increases uniformly by a fixed number each year, in which year will the production be $1400$ units?

Find the value of $k$ if $k+9, 2k-1,$ and $2k+7$ are three consecutive terms of an Arithmetic Progression.

If $\frac{1}{2}, \frac{1}{3}, \frac{1}{6}, ...$ are in AP, find the 9th term of the sequence.

If $a, b, c, d, e$ are five consecutive terms of an AP, find the value of $a-4b+6c-4d+e$.

If the $n^{th}$ terms of the APs $23, 25, 27, \dots$ and $5, 8, 11, \dots$ are equal, find the value of $n$.

If $x+1, 3x, 4x+2$ are three consecutive terms of an AP, find the $10^{th}$ term.

Calculate the sum of the first $6$ terms of an AP where $a = 1$ and $d = 2$.

Find the sum of the first $5$ terms of the progression: $3, 7, 11, \dots$

An AP begins with $25$ and has a common difference of $-5$. Find the sum of the first $6$ terms.

Determine the sum of the first $6$ terms of the AP: $0, 1, 2, \dots$

Find the sum of the first $20$ terms of the AP: $0.6, 1.7, 2.8, \dots$

If the sum of the first $n$ terms of an AP is $S_n = 5n^2 + 3n$, find the common difference of the AP.

The ratio of the sum of the first $n$ terms of two APs is $(3n + 8) : (7n + 15)$. Find the ratio of their $12^{th}$ terms.

If $S_n = n(4n+1)$, find the common difference.

Find the sum of all integers between 100 and 200 that are divisible by 9.

If the sum of the first $10$ terms of an AP is $210$ and the sum of the first $20$ terms is $820$, find the first term $a$.

A heavy-duty bulb has a life of $2,000$ hours. If it is used for $5$ hours on the first day and the usage increases by $15$ minutes ($0.25$ hours) each day, how many hours will it be used on the $21^{st}$ day?

In a cricket tournament, the prize money for the winner is ₹$5,000$ and decreases by ₹$400$ for each subsequent rank. What is the prize money for the $6^{th}$ rank?

A clerk is paid ₹$250$ for the first day and ₹$10$ more for each succeeding day. How much will he be paid for the $31^{st}$ day?

A machine costs ₹$5,00,000$. If its value depreciates by ₹$25,000$ every year, what will be its value after $10$ years?

The heart rate of an athlete decreases by $4$ beats per minute every minute after finishing a race. If the heart rate was $160$ bpm immediately after the race, how many minutes will it take to drop to $80$ bpm?

A company's profits increase by $₹ 2$ lakhs every year. If the profit in the $5^{th}$ year was $₹ 20$ lakhs, what was the total profit over the first $10$ years?

A pendulum's swing length decreases by $2$ cm each time. If the first swing is $40$ cm, what is the length of the $15^{th}$ swing?

A sum of ₹$1,000$ is used to award $5$ prizes such that each prize is ₹$20$ more than the preceding one. What is the value of the smallest prize?

In a garden, a laborer is asked to plant trees in a row. He plants $5$ trees in the first hour, and in each subsequent hour, he plants $3$ more trees than in the previous hour. If he worked for $8$ hours, find the total number of trees planted.

A sum of ₹$1,000$ is invested at $8\%$ simple interest per year. The interests at the end of each year form an AP. Calculate the interest at the end of $30$ years.

What is the $5^{th}$ term of the AP: $10, 5, 0, -5, \dots$?

Identify the common difference of the AP: $\sqrt{3}, 2\sqrt{3}, 3\sqrt{3}, \dots$.

In the formula $a_n = a + (n-1)d$, what must $n$ always be?

If $d = -2$ and $a_{10} = 0$, what is the first term $a$?

If the common difference of an Arithmetic Progression is $d$, what is the value of $a_n - a_{n-k}$?

The $n^{th}$ term of an Arithmetic Progression is given by $a_n = a + (n-1)d$. If $a=10$ and $d=-3$, find the $12^{th}$ term.

Two Arithmetic Progressions have the same common difference. The first term of one of these is $-1$ and that of the other is $-8$. Then the difference between their $4^{th}$ terms is:

Find the number of all two-digit natural numbers which are divisible by 7.

If $k-1, k+3, 3k-1$ are in AP, find the value of the 5th term.

What is the 11th term of an AP whose 3rd term is -3 and common difference is 4?

Find the common difference of an AP whose $n^{th}$ term is $a_n = n + 5$.

What is the sum of the first $5$ terms of the AP where $a=10$ and $l=20$?

In an AP, if $a=3$ and $d=2$, what is $a_{12}$?

If the sum of the first $n$ terms is $n^2$, what is the $10^{th}$ term?

Which term of the Arithmetic Progression $24, 23\frac{1}{3}, 22\frac{2}{3}, 22, \dots$ is its first negative term?

Find the $10^{th}$ term of the AP $\sqrt{2}, \sqrt{8}, \sqrt{18}, \dots$

Determine the value of $k$ such that $2k, k+10, 3k+2$ are in AP.

What is the common difference of an AP in which $a_{21} - a_7 = 84$?

If $a, b, c$ are in AP, then the terms $(b + c - a), (c + a - b), (a + b - c)$ are in:

The ratio of the $7^{th}$ to the $3^{rd}$ term of an AP is $12:5$. Find the ratio of the $13^{th}$ to the $4^{th}$ term.

If the common difference of an AP is $3$, find the $10^{th}$ term if the first term is $2$.

In an AP, if $a_n = 9 - 5n$, find the first term $a_1$.

Find the $20^{th}$ term of the AP: $7, 13, 19, \dots$

If $a=10$ and $d=10$, what are the first four terms of the AP?

What is the sum of the two middlemost terms of the Arithmetic Progression $-\frac{4}{3}, -1, -\frac{2}{3}, \dots, \frac{13}{3}$?

If the $6^{th}$ term of an AP is $2$ and the $10^{th}$ term is $-10$, find the $15^{th}$ term.

Find the $25^{th}$ term of the AP $-5, -5/2, 0, 5/2, \dots$.

Find the $n^{th}$ term of an AP if the sum of its first $n$ terms is $S_n = 2n^2 + 3n$.

If $k+2, 4k-6$, and $3k-2$ are three consecutive terms of an AP, find the value of $k$.

In an AP, if the $m^{th}$ term is $n$ and the $n^{th}$ term is $m$, find the $r^{th}$ term.

What is the sum of the first $3$ terms of the AP: $-2, -4, -6, \dots$?

Find the sum of the first $5$ even natural numbers.

Calculate the sum of the first $10$ multiples of $1$.

Find $S_3$ for the sequence $10, 20, 30, \dots$.

A sum of $₹ 700$ is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is $₹ 20$ less than its preceding prize, what is the value of the smallest prize?

Find the sum of all three-digit natural numbers which are multiples of 11.

Find the sum of the first 15 terms of the AP: $10, 7, 4, \dots$

If $S_n$ denotes the sum of $n$ terms of an AP, and $\frac{S_m}{S_n} = \frac{m^2}{n^2}$, find $\frac{a_m}{a_n}$.

How many terms of the AP $-6, -11/2, -5, \dots$ are needed to give the sum $-25$?

The first and last terms of an AP are $a$ and $l$. If $S$ is the sum of all the terms, find the common difference $d$ in terms of $a, l, S$.