Q1. The nth term of an AP is 6n + 2. Find its common difference.

Solution 1

Q2. The first term of an AP is p and its common differenceis q. Find its 10th term.

Solution 2.

Q3. Find the next term of AP `sqrt{2}`, `sqrt{8}`, `sqrt{18}`,

Solution 3.

Q4. Which term of an AP 14, 11, 8,… is -1 ?

Solution 4

Q5. Write the next two terms of the AP: 1, -1, -3, -5….

Solution 5

Q6. In the following situation, form an AP: Thetaxi fareafter each km when theface is Rs. 15 for the firstkm and Rs. 8 for each additional km.

Solution 6

Q7. Find the 11th term of the AP – 3, -`frac{1}{2}`, 2,…

Solution 7

Q8. Find the 6th term from the end of the AP 17, 14,11,…,-40

Solution 8

Q9. Find the 12th term of an AP with first term 9 and common difference 10.

Solution 9

Q10. Which term of the AP 3, 15, 27, 39,…will be 120 more than its 21st term?

Solution 10

Q11. Find the number of two- digit numbers which are divisible by 6.

Solution 11

Q12. In an AP, the first term is 12 and common difference is 6. If the last term of the AP is 252, find its middle term.

Solution 12

Q13. Find the number of three- digit natural numbers which are divisible by 11.

Solution 13

Q14. Find `a_{30}` – `a_{20}` for the AP (i) -9, -14, – 19, -24,…(ii)a, a + d, a + 2d, a + 3d,…

Solution 14

Q15. Two APs have the same common difference. The first term of one of theses is 3 and that of the other is 8. What is the difference between their (i) 2nd terms? (ii) 4th terms? (iii) 10th terms? (iv) 20th terms?

Solution 15

Q16. The third term of an AP is p and fourth term is q. Find the 10th term.

Solution 16

Q17. Which term of an AP 5, 2, – 1,…is -22?

Solution 17

Q18. The fifth term of an AP is 1, whereas its 31st term is -77. Which term of the AP is – 17?

Solution 18

Q19. The 8th term of an Arithmetic Progression is 37 and its 12th term is 57. find the AP.

Solution 19

Q20. The 8th term of an arithmetic progression is zero. Prove that its 38th term is triple of its 18th term.

Solution 20

Q21. The 19th term of an AP is equal to three times its sixth term. If its 9th term is 19, find the AP.

Solution 21

Q22. Which term of the sequences 17, 16 `frac{1}{5}`, 15 `frac{2}{5}`, 14 3`frac{3}{5}`,… is the first negative term?

Solution 22

Q23. Find a, b and c such that the following numbers are in AP: a, 7, b, 23,c.

Solution 23

Q24. The eighth term of an AP is half its second term and the eleventh term exceeds one- third of its fourth term by 1. Find the 15th term.

Solution 24