Mastering Arithmetic Progressions: A Class 10 NCERT Practice Quiz

Q1. Which of the following is an Arithmetic Progression?

Q2. What is the common difference of the AP: $1/3, 5/3, 9/3, 13/3, \dots$?

Q3. The $n^{\text{th}}$ term of an AP is given by $a_n = 3 + 4n$. The common difference is:

Q4. If the first term of an AP is $5$ and the common difference is $3$, find the $10^{\text{th}}$ term.

Q5. Which term of the AP $21, 18, 15, \dots$ is $-81$?

Q6. How many two-digit numbers are divisible by $3$?

Q7. Find the sum of the first $20$ terms of the AP: $1, 4, 7, 10, \dots$.

Q8. The $17^{\text{th}}$ term of an AP exceeds its $10^{\text{th}}$ term by $7$. The common difference is:

Q9. If $x+1, 3x, 4x+2$ are in AP, find the value of $x$.

Q10. The sum of the first $15$ multiples of $8$ is:

Q11. The sum of the first $n$ terms of an AP is $S_n = 2n^2 + 5n$. Find its $n^{\text{th}}$ term.

Q12. If the sum of the first $7$ terms of an AP is $49$ and that of $17$ terms is $289$, find the sum of the first $n$ terms.

Q13. If the $m^{\text{th}}$ term of an AP is $1/n$ and the $n^{\text{th}}$ term is $1/m$, then its $(mn)^{\text{th}}$ term is:

Q14. The sum of all natural numbers between $100$ and $200$ which are divisible by $6$ is:

Q15. If the $p^{\text{th}}$ term of an AP is $q$ and the $q^{\text{th}}$ term is $p$, then the $r^{\text{th}}$ term is: