CBSE - 10th - A.PSeries Practice Sheet

Arithmetic Progression (A.P)

Practice Sheet

 

1. Which of the following sequences are in arithmetic progression (A.P.)?

(i)             27, 23, 18, 15, 11, ... (ii) a, a + 2b, a + 4b, a + 8b, a + 10 b,

 (iii) a + b, (a + 1) + b, (a + 1) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2) + ...

2. The nth term of an A.P. is 2n + 3. Is the sequence, so formed, in A.P.? If so, find its 8th term.
3. The nth term of an A.P. is 3n – 4. Is the sequence, so formed, in A.P? If so, find its14th term.
4. The nth term of an A.P. is 3n² + 4. Is the sequence so formed in A.P.?
5. Show that R – 7, R – 10, R – 13, R – 16, R – 19 ... are in A.P. find its 8th term and the common difference.
6. Each term of an A.P. is doubled . Is the resulting sequence also, in A.P.? If so, find its 1st term and its common difference.
7. Find the 15th, 22th and nth term of the A.P. given by 2, 8, 14, 20, .....
8. Find the 15th term from the end of the A.P. 3, 5, 7, 9, ...., 201.
9. Which term of the A.P. 12, 7, 2, – 3, .... is – 98 ?
10. The 1st term of an A.P. is – 7. The common difference is 6 and the last number is 293. Find the number of terms.
11.  An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find the 34th term.
12. The third term of an A.P. is P and fourth term is q, find the tenth term and the general term.
13. The 8th term of an A.P. is zero, prove that its 38th term is triple the 18th term.
14. The 1st term of an A.P. is – 54 and sixteenth term is 21. Find the 12th term.
15. The 8th and 24th terms of an A.P. are 45 and 157 respectively, find the 33rd term.
16. How many numbers of two digits are divisible by 6?
17. How many numbers of two digits are divisible by 9?
18. Evaluate :

(i)             4 + 3 + 8 + 5 + 12 + 7 + ... 32 terms.

(ii)            3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + ... to 35 terms.

19. Find the sum of all numbers, which are divisible by 7 and lying between 50 and 500.
20. Find the sum of all integers between 92 and 786, which are multiples of 9.
21. Find the sum of all natural numbers between 100 and 1000, which are multiples of 5.
22. Find the sum of all odd integers between 300 and 498.
23. Find the sum of all integers between 400 and 579, which are divisible by 10.
24. How many terms of the sequence – 12, – 9, – 6, – 3, .... must be taken to make the sum 54?
25. In an A.P., if the 12th term is – 13 and the sum of first four terms is 24, what is the sum of the first 10 terms?
26. The fourth term of an A.P. is 11 and the eighth term exceeds twice the fourth term by 5. Find the A.P. and sum of first 20 terms.
27. Determine, the sum of first 35 terms of an A.P., if second term is 2 and the seventh term is 22.
28. Ravi spent  Rs. 120 during first month, Rs. 150 in the next month, Rs. 180 in the third month. If he continues to spend in this sequence, in how many months, will he spent Rs. 1800 ?
29. A manufacturer of  dinner sets, produced 250 sets in the fourth month and 400 sets in the seventh month. Assuming that the production uniformly increases by a fixed number every month, find

           (i)             the production in the 6th month.
           (ii)            total production in 10 months.
          (iii)           production in 10th month.
          (iv)          production in 8 months.

30. Raman buys a washing machine for Rs. 10000. He pays Rs. 2000 in cash and agrees to pay the  balance in instalments of Rs. 500 plus 10% interest on the unpaid amount. Find the total amount paid for the washing machine.