EXTRA QUESTIONS OF AP SET-3

PODAR INTERNATIONAL SCHOOL (CBSE)

Practice Sheet

Std : X Subject: Mathematics

Topic: Arithmetic Progression 

1. In the following APs find the missing terms
(i) 2,____ , 26
(ii) 5,____ ,_____ , 9 (1/2)

2. Find a3, a5 and a8, if an = ( - 1)n × n + 1


3. Find the 21st and 42 nd terms of the sequence defined by
tn = 0, if n is odd.AND 1, if n is even

4. Find the sum of n terms of the sequence {an } where an = 5 - 6n , n Belongs to N

5. Find the 27 th and the nth terms of the sequence 5, 2, -1,- 4, -7, .....

6. A sequence { an } is given by the formula an = 10 - 3n. Prove that it is an A.P.

7 .If m times the m th term of an A. P. is equal to n times its n th term, prove that
( m + n ) th term of an A. P. is zero. [ Delhi 2004 ]


8. Find 10th term from each end of an A.P. 5, 7......, 159.

9. How many terms are there in an A.P. whose first and fifth terms are - 14 and 2 respectively
and the sum of the terms is 40?


10. The 4th term of an AP is equal to 3 times the first term and the 7th term exceeds twice the
third term by 1. Find the 1st term and the AP.

11. Find the sum of all three digit numbers which leave the remainder 3 when divided by 5.
4 marks questions:

12. Amrita buys a house for ` 22,000.She pays `4,000 cash and agrees to pay the balance in
annual installments of ` 1,000 plus 10 % interest on the unpaid amount. What will the house
cost for her?

13. How many terms of the A.P. - 6 , -11/2,- 5 , are needed to give the sum -25? Explain the
double answer.

14. If the p th, q th, r th terms of an A.P. be x, y, z respectively. Show that
x ( q - r ) + y ( r - p ) + z ( p - q) = 0

15. Find the sum of 32 terms of an A.P. whose third term is 1 and 6th term is -11.

16. Find the 17th term and the nth term of A.P
3, 3 + √2 , 3 + 2 √2 , 3 + 3 √2....

17. Supreet deposits a sum of ` 5000 in State Bank of India. Bank pays simple interest of 5 % per
annum on the money deposited. Calculate the interest at the end of 1, 2, 3,.... years .Verify that
the sequence of interest forms an AP. Also find the interest earned after 40 years by using the
idea of AP.

18. A contract on construction job specifies a penalty for delay of completion beyond certain date
as follows : `200 for the first day,`250 for the second day, `300 for the third day, etc. , the
penalty for each succeeding day being `50 more than for the preceding day. How much
money the contractor has to pay as penalty if he has delayed the work by 30 days?
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