Arithmetic Progression Assignments for Class X CBSE Mathematics Sample Test Paper
Q. 1. Find the roots: (x + 2) / (x – 2) + (x – 2) / (x + 2) = 5/2, x ≠2, x≠ -2
Q. 2. Determine the values of p for which the quadratic equation: 2×2 + p x + 8 = 0 has real roots.
Q. 3. A shopkeeper buys a number of bananas for Rs. 600. If he had bought 10 dozen more bananas for the same amount, each dozen would have cost him Rs. 2 less. Find the number of bananas bought by him.
Q. 4. If the roots of the equation (c2 – ab)x2 – 2(a2 – bc) x + b2-ac = 0 are equal, prove that either a=0 or a3 + b3 + c3=3abc
Q. 5. Find three consecutive positive integers whose product is equal to sixteen times their sum.
Q. 6. A fraction becomes 6/5 if 1 is added to each of the numerator and the denominator. However, if we subtract 5 from each, the fraction becomes 3/2. find the fraction.
Q. 7. For what value of k, the system of equations: 2x – ky + 3 = 0, 4x + 6y – 5 = 0 is consistent?
Q. 8. Solve graphically: x + 4y = 10, y + 3x = 8.
Q. 9. If a1, a2, a3, a4, a5,…… are the n terms of an A.P. Derive the formula for its nth term.
Q. 10. If a1, a2, a3, a4, a4,…… are the n terms of an A.P. Derive the formula for the sum of its n terms.
Q. 11. If nth term of an A.P. is given by an = 5n – 3. Find the sum of its 50 terms.
Q. 12. Sum of n terms of a sequence is given by Sn = 2n2 – 2n. If it is an A.P. then find its 20th term.
Q. 13. Find the sum of the following series: 10 + 14 + 18 + 22 + …………104
Q. 14. If the sum of first 13 terms of an A.P. is 91 and sum of its first 30 terms is 465. Find the sum of its 50 terms.
Q. 15. The sum of three numbers which are in A.P. is 9 and sum of their squares is 35. Find the numbers.
Q. 16. Divide 32 into 4 parts such that they are in AP and the ratio of the product of first term and fourth terms = product of second and third terms is equal to 7/15.
Q. 17. If the pth,qth,rth terms of an AP are a,b,c then prove a(q – r) + b(r-p) = c (q – p)
Q. 18. If pth term of an A.P be 1/q and the qth term be 1/p, show that the sum of pq terms is
Q. 19. The sum of n terms of an A.P. is given by Sn = 5n2 + 3n, find the nth term of A.P.
Q. 20. How many terms of the A.P. -6, -11/2, -5, ………are needed to give the sum -25? Explain the double answer.
Q. 21. Find the 30th and 60th terms of the following sequence:
(1) 13, 18, 23, 28, 33,………. (2) -10, -7, -4, -1……………..
Q. 22. Find the sum of the following series: 1. 3+8+13+18+23 …………………….248 2. -10, -15, -20, -25,………….-105
Q. 23. The sum of three numbers which are in A.P. is 9 and sum of their squares is 35. Find the numbers.
Q. 24. nth term of a sequence is given by the formula an = 10-3n, find the sum of its 20 terms.
Q. 25. The 8th term of an A.P. is 32 and its 12th term is 52. Find the A.P.
Q. 26. 500 logs are stacked in a way such that 32 logs in the bottom row, 31 in the next row, 30 in the row next to it and so on. In how many rows are the 500 logs placed and how many logs are in the top row?
Q.27. Which of the following sequences are A.P’S? Write down their common difference.
(a) 5, 10, 15, 20,25………..(b) 2, 2, 2, 2,2……………..(c) 2, 4, 8, 16,32…………..
Q.28. Write next two terms of given A.P. (a) -3, -5, -7,-9…………..
Q.29. Find 10th term of given A.P. 10, 20, 30, 40…………
Q.30. Find 20th term of A.P. whose first term = 10, c.d = 3
Q.31. Find n, if the given value of x is nth term of A.P. 17, 22, 27, 32… x = 267
Q.32. Find for the A. P. 3, 14, 25, 36………
Q.34. Third term of an A.P. is 21 and the eighth term is 56.Find A.P. and also find its eleventh term.
Q.35. 3 times the tenth term is equal to 5 times the twentieth term. Find twentieth term.
Q.36. Find the sum 2+4+6+…………+202
Q.37. Write sequence with nth term 5+2 n. Find sum of first 20 terms.
Q.38. Find sum of all natural numbers between 1 and 98 which are multiples of 6.
Q.39. How many terms of the series must be added to get sum 55,15, 13, 11, 9,……
Q.40. Sum of terms of A.P. is 36 and product is 1296. Find A.P
Q. 2. Determine the values of p for which the quadratic equation: 2×2 + p x + 8 = 0 has real roots.
Q. 3. A shopkeeper buys a number of bananas for Rs. 600. If he had bought 10 dozen more bananas for the same amount, each dozen would have cost him Rs. 2 less. Find the number of bananas bought by him.
Q. 4. If the roots of the equation (c2 – ab)x2 – 2(a2 – bc) x + b2-ac = 0 are equal, prove that either a=0 or a3 + b3 + c3=3abc
Q. 5. Find three consecutive positive integers whose product is equal to sixteen times their sum.
Q. 6. A fraction becomes 6/5 if 1 is added to each of the numerator and the denominator. However, if we subtract 5 from each, the fraction becomes 3/2. find the fraction.
Q. 7. For what value of k, the system of equations: 2x – ky + 3 = 0, 4x + 6y – 5 = 0 is consistent?
Q. 8. Solve graphically: x + 4y = 10, y + 3x = 8.
Q. 9. If a1, a2, a3, a4, a5,…… are the n terms of an A.P. Derive the formula for its nth term.
Q. 10. If a1, a2, a3, a4, a4,…… are the n terms of an A.P. Derive the formula for the sum of its n terms.
Q. 11. If nth term of an A.P. is given by an = 5n – 3. Find the sum of its 50 terms.
Q. 12. Sum of n terms of a sequence is given by Sn = 2n2 – 2n. If it is an A.P. then find its 20th term.
Q. 13. Find the sum of the following series: 10 + 14 + 18 + 22 + …………104
Q. 14. If the sum of first 13 terms of an A.P. is 91 and sum of its first 30 terms is 465. Find the sum of its 50 terms.
Q. 15. The sum of three numbers which are in A.P. is 9 and sum of their squares is 35. Find the numbers.
Q. 16. Divide 32 into 4 parts such that they are in AP and the ratio of the product of first term and fourth terms = product of second and third terms is equal to 7/15.
Q. 17. If the pth,qth,rth terms of an AP are a,b,c then prove a(q – r) + b(r-p) = c (q – p)
Q. 18. If pth term of an A.P be 1/q and the qth term be 1/p, show that the sum of pq terms is
Q. 19. The sum of n terms of an A.P. is given by Sn = 5n2 + 3n, find the nth term of A.P.
Q. 20. How many terms of the A.P. -6, -11/2, -5, ………are needed to give the sum -25? Explain the double answer.
Q. 21. Find the 30th and 60th terms of the following sequence:
(1) 13, 18, 23, 28, 33,………. (2) -10, -7, -4, -1……………..
Q. 22. Find the sum of the following series: 1. 3+8+13+18+23 …………………….248 2. -10, -15, -20, -25,………….-105
Q. 23. The sum of three numbers which are in A.P. is 9 and sum of their squares is 35. Find the numbers.
Q. 24. nth term of a sequence is given by the formula an = 10-3n, find the sum of its 20 terms.
Q. 25. The 8th term of an A.P. is 32 and its 12th term is 52. Find the A.P.
Q. 26. 500 logs are stacked in a way such that 32 logs in the bottom row, 31 in the next row, 30 in the row next to it and so on. In how many rows are the 500 logs placed and how many logs are in the top row?
Q.27. Which of the following sequences are A.P’S? Write down their common difference.
(a) 5, 10, 15, 20,25………..(b) 2, 2, 2, 2,2……………..(c) 2, 4, 8, 16,32…………..
Q.28. Write next two terms of given A.P. (a) -3, -5, -7,-9…………..
Q.29. Find 10th term of given A.P. 10, 20, 30, 40…………
Q.30. Find 20th term of A.P. whose first term = 10, c.d = 3
Q.31. Find n, if the given value of x is nth term of A.P. 17, 22, 27, 32… x = 267
Q.32. Find for the A. P. 3, 14, 25, 36………
Q.34. Third term of an A.P. is 21 and the eighth term is 56.Find A.P. and also find its eleventh term.
Q.35. 3 times the tenth term is equal to 5 times the twentieth term. Find twentieth term.
Q.36. Find the sum 2+4+6+…………+202
Q.37. Write sequence with nth term 5+2 n. Find sum of first 20 terms.
Q.38. Find sum of all natural numbers between 1 and 98 which are multiples of 6.
Q.39. How many terms of the series must be added to get sum 55,15, 13, 11, 9,……
Q.40. Sum of terms of A.P. is 36 and product is 1296. Find A.P
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