CBSE Important Questions

Q. 1. Find the 10^th term of the AP : 2, 7, 12,………………………………………….

Q. 2. Find the 30^th term of the AP: 10, 7, 4,………………………………………….

Q. 3. Find the 11^th term of the AP: -3, -1/2, 2,………………………………………

Q. 4. The 7^th term of an AP is – 4 and 13^th term is – 16. Find the AP and nth term.

Q. 5. Find the 31st term of an AP whose 11^th term is 38 and 16^th term is 73.

Q. 6. Determine the AP whose 3rd term is 5 and 7^th term is 9.

Q. 7. Determine the AP whose third term is 16 and 7^th term exceed the 5^th term by 12.

Q. 8. The 17^th term of an AP exceeds its 10^th term by 7. Find the common difference.

Q. 9. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29^th term.

Q. 10. The sum of the 4^th and 8^th terms of an AP is 24 and the sum of the 6^th and 10^th term is 44. Find the first three terms of the AP.

Q. 11.

1. Find the 11the term from the last term of the AP: 10, 7, 4,……., -62
2. Find the 20^th term from the last term of the AP: 3, 8, 13,………………, 253.
3. Find the 10^th term from the end of the AP: 8, 10, 12,,,,,,,,,,,,,,,,,,,,,,126.

Q. 12. If the 8^th term of an AP is 31 and 15^th term is 16 more than the 11^th term, find the AP.

Q. 13. The n^th term of an AP is 7 – 4n. Find its common difference.

Q. 14.Write the next two term of the AP: √8, √18, √32,……….

Q. 15. The first term of an AP is p and its common difference is q. Find its 10^th term.

Q. 16. The sum of the 5^th and 7^th terms of AP is 52 and the 10^th term is 46. Find the AP.

(TYPE II)

Q. 1. Find the number of terms in each of the following APs:

1. 7, 13, 19,……………………….,205
2. 18, 15½ , 13,………………………………….,-47.

Q. 2.

1. Check whether -150 is a term of the AP:  11, 8, 5, 2,………………………………………
2. Check whether 301 is a term of the list of numbers, 5, 11, 17, 23,…………………….

Q. 3.

1. Which term of the AP: 3, 8, 13, 18,…………………………. Is 78?
2. Which term of the AP: 3, 15, 27, 39,……. will be 132 more than its 54th term?
3. Which term of the Arithmetic Progression 3, 10, 17, …………… will be 84 more than its 13^th term?
4. If the 3rd and 9^th terms of an AP are 4 and – 8 respectively, which term of this AP is 0?

Q. 4. Find k, if the given value of x is the k^th term of the given AP

25, 50, 75,…………………………… x = 1000
5½, 11, 16½……………………….. x = 550

Q. 5. (a). How many two-digit numbers are divisible by 3?
(b). How many three-digit numbers are divisible by 7?
(c). How many multiples of 4 lie between 10 and 250?
(d). How many natural numbers between 100 and 200, which are divisible by 4.
(e). How many natural numbers less than 200 which are divisible by 6.
(f). How many natural numbers between 100 and 500, which are divisible by 8

Q. 6. For what value of n, are the nth terms of two APs: 63, 65, 67,………… and 3, 10 17,……………….. equal ?

Q. 7. Subba Rao started work in 2001 at annual salary of Rs. 10,000 and received an increment of Rs. 500 each year. In which year did his income reach Rs. 15,000?

Q. 8. Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week, her weekly savings become Rs. 20.75, find n,

Q. 9. In a flower bed, there are 23 rose plants in the first row, 21 in the second row, 19 in the third row, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?

EXTRA:-

Q. 1. A sum of Rs. 1,000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these interests form an AP? If so, find the interest at the end of 30 years making use of this fact.

Q. 2. (a). Which term of the AP: 121, 117, 113,……… is its first negative term?
(b). Which term of the sequence 114, 109, 104,……… is the first negative term?
(c) Which term of the AP,: 17, 16½, 16, if the first negative term?

Q. 3. (1). The 8^th term of an AP is zero. Prove that its 38^th term is triple its 18^th term.

1. The 4^th term of an AP is zero. Prove that its 25^th term is triple its 11^th term.
2. The 6^th term of an AP is zero. Prove that its 21st term is triple its 11^th term.
3. If fif^th term of an AP is zero., show that its 33rd term is four times its 12^th term.
4. If 7 times of 7^th term of an AP is equal to 11 times of 11^th term, show that the 18^th term of the AP is zero.
5. If the 8^th term of an AP is zero, prove that its 20^th term is thrice its 12^th term.

Q. 4. Fill in the blank in the following table, given than a is the first term, d the common difference and an the n^th term of the AP: