Arithmetic Progressions

CBSE Class 10 Mathematics · every board question from this chapter, 2022–2026

• The n^th term of an A.P. is √2 n+1. Its common difference is2026
• In an A.P., if a_14-a_8=24, then the common difference of the A.P. is2026
• The value of x for which 2 x,(x+10) and (3 x+2) are the three consecutive terms of an A.P. is:2026
• The common difference of the AP: √2, 2 √2, 3 √2, 4 √2, ….. is:2026
• Which of the following sequence is not an A.P.?2026
• The first term of an AP is p and the common difference is q, then its 10th term is:2026
• If a_n represents n^th term of the A.P. -15/4,-10/4,-5/4, ….. then value of a_16-a_12 is2026
• The n^th term of the A.P. -1/3, 2/3, 5/3, 8/3, … is:2026
• If sum of first ten terms of an A.P. is zero with a as the first term and d, the common difference, which of the following…2026
• In an A.P., a=-3 and S_17=357. The value of a_17 is2026
• In an A.P., the first term is 32 and the last term is - 10. If the common difference is -2, then find the number of terms and…2026
• In an A.P., the first term is 4 and the last term is 31. If sum of all the terms is 175, find the number of terms and the common…2026
• In an A.P., 15^th term exceeds the 8^th term by 21. If sum of first 10 terms is 55, then form the A.P. OR The sum of first n…2026
• Find two consecutive negative integers, sum of whose squares is 481.2026
• A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 km/hr less…2026
• 'Kolam' is a decorative art which is made with rice flour in South Indian States. It is drawn on grid pattern of dots. One such…2026
• In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are arranged 3…2026
• Your elder brother wants to buy a car and plans to take a loan from a bank for his car. He repays his total loan of ₹ 1,18,000 by…2026
• 'Kolam' is a decorative art which is made with rice flour in South Indian States. It is drawn on grid pattern of dots. One such…2026
• The 9^th term from the end (towards first term) of the AP 7,11,15,19, …., 147 is:2025
• Three numbers in AP have the sum 30. What is its middle term?2025
• If the sum of first m terms of an AP is 2 m^2+3 m, then its second term is:2025
• The 10^th term of the AP 5, 19/4, 9/2, 17/4, … is:2025
• The 11^th and 13^th term of an AP are 39 and 45, respectively. What is the common difference of the AP?2025
• Assertion (A): Common difference of the AP: 5,1,-3,-7, … is 4. Reason (R): Common difference of the AP: a_1, a_2, a_3, …, a_n is…2025
• Assertion: For an A.P., 3,6,9, …, 198,10^th term from the end is 168. Reason (R): If 'a' and ' l ' are the first term and last…2025
• Find the sum of all 3-digit natural numbers which are divisible by 11.2025
• A sum of ₹ 2,000 is invested at 7 % per annum simple interest. Calculate the interests at the end of 1^st, 2^nd and 3^rd year. Do…2025
• An AP consists of 'n' terms whose n^th term is 4 and the common difference is 2. If the sum of ' n ' terms of AP is -14, then…2025
• The sum of the third term and the seventh term of an AP is 6 and their product is 8. Find the sum of the first sixteen terms of…2025
• A school is organizing a charity run to raise funds for a local hospital. The run is planned as a series of rounds around a…2025
• Cable cars at hill stations are one of the major tourist attractions. On a hill station, the length of cable car ride from base…2025
• In order to organise, Annual Sports Day, a school prepared an eight lane running track with an integrated football field inside…2025
• In an equilateral triangle of side 10 cm, equilateral triangles of side 1 cm are formed as shown in the figure below, such that…2025
• The next (4^th ) term of the A.P. √18, √50, √98, … is:2024
• In an A.P., if the first term (a)=-16 and the common difference (d)=-2, then the sum of first 10 terms is:2024
• The common difference of the A.P. 1/(2 x), (1-4 x)/(2 x), (1-8 x)/(2 x) is:2024
• The common difference of an A.P. in which a_15-a_11=48, is2024
• The next (4^th ) term of the A.P. √7, √28, √63, … is:2024
• In an A.P., if the first term a=7, n th term a_n=84 and the sum of first n terms s_n=2093/2, then n is equal to:2024
• The common difference of an A.P. in which a_20-a_15=20, is2024
• The 14^th term from the end of the A.P. -11,-8,-5, …, 49 is:2024
• The number of terms in the A.P. 3,6,9,12, …, 111 is:2024
• Three numbers in A.P. have the sum 30. What is its middle term?2024
• Which term of the A.P. -29, -26, -23,....., 61 is 16?2024
• If the sum of first n terms of an A.P. is 3 n^2+4 n and its common difference is 6, then its first term is:2024
• n th term of an A.P. is 7 n+4. The common difference is:2024
• If the first three terms of an A.P. are 3 p-1,3 p+5,5 p+1 respectively; then the value of p is:2024
• If 2 x+y=13 and 4 x-y=17, find the value of (x-y). OR Sum of two numbers is 105 and their difference is 45. Find the numbers.2024
• If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289, find the sum of its first 20 terms. OR The ratio…2024
• If the sum of first m terms of an A.P. is same as sum of its first n terms (m ≠ n), then show that the sum of its first (m+n)…2024
• If the sum of the first 14 terms of an A.P. is 1050 and the first term is 10, then find the 20^th term and the n^th term. OR The…2024
• A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was ₹ 15,000 after 4…2024
• The sum of first and eighth terms of an A.P. is 32 and their product is 60. Find the first term and common difference of the A.P.…2024
• Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover hidden…2024
• If k+2,4 k-6 and 3 k-2 are three consecutive terms of an A.P., then the value of k is:2023
• The next term of the A.P.: √6, √24, √54 is:2023
• The common difference of the A.P. whose n^th term is given by a_n=3 n+7, is:2023
• The 13^th term from the end of the A.P.: 20,13,6,-1, …..,-148 is:2023
• If p-1, p+1 and 2 p+3 are in A.P., then the value of p is2023
• The next term of the A. P.: √7, √28, √63 is:2023
• If a, b, c form an A.P. with common difference d, then the value of a - 2b - c is equal to2023
• The 11^th term from the end of the A.P.: 10,7,4, … ….,-62 is:2023
• If the sum of the first n terms of an A.P be 3 n^2+n and its common difference is 6, then its first term is2023
• The common difference of the A.P. whose n^th term is given by a_n=5 n-7 is:2023
• Assertion: a, b, c are in A.P. if and only if 2 b=a+c. Reason (R): The sum of first n odd natural numbers is n^2.2023
• Half of the difference between two numbers is 2. The sum of the greater number and twice the smaller number is 13. Find the…2023
• How many terms are there in an A.P. whose first and fifth terms are - 14 and 2, respectively and the last term is 62. OR Which…2023
• If p^th term of an A.P. is q and q^th term is p, then prove that its n^th term is (p+q-n).2023
• The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20^th term. OR Rohan repays his total loan of ₹…2023
• How many terms are there in A.P. whose first and fifth term are - 14 and 2, respectively and the last term is 62. OR Which term…2023
• In an A.P., the sum of the first n terms is given by S_n=6 n-n^2. Find its 30^th term.2023
• Find the common difference of an A.P. whose first term is 8, the last term is 65 and the sum of all its terms is 730.2023
• How many terms of the arithmetic progression 45, 39, 33, must be taken so that their sum is 180? Explain the double answer.2023
• The sum of first seven terms of an A.P. is 182. If its 4^th term and the 17^th term are in the ratio 1: 5, find the A.P. OR The…2023
• Prerna saves ₹ 32 during the first month, ₹ 36 in the second month and ₹ 40 in the third month. If she continues to save in this…2023
• The ratio of the 11^th term to the 18^th term of an A.P. is 2: 3. Find the ratio of the 5^th term to the 21 ^st term. Also, find…2023
• Solve the equation for x: 1+4+7+10+….+x=2872023
• The ratio of the 11^th term to 17^th term of an A.P. is 3: 4. Find the ratio of 5^th term to 21^st term of the same A.P. Also,…2023
• Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per…2023
• A coaching institute of Mathematics conducts classes in two batches I and II and fees for rich and poor children are different.…2023
• Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per…2023
• Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per…2023
• Find the sum of first 30 terms of AP: - 30, - 24, - 18,...... OR In an AP if S_n=n(4 n+1), then find the AP.2022
• Which term of the A.P. -11/2,-3,-1/2, … is 49/2? OR Find a and b so that the numbers a, 7, b, 23 are in A.P.2022
• Find the sum of first 20 terms of an AP in which d=5 and a_20=135.2022
• Find the sum of the first twelve 2-digit numbers which are multiples of 6. OR In an AP, if a_2=26 and a_15=-26, then write the AP.2022
• In an A.P. if the sum of third and seventh term is zero, find its 5^th term. OR Determine the A.P. whose third term is 5 and…2022
• Find the common difference 'd' of an AP whose first term is 10 and the sum of the first 14 terms is 1505.2022
• Find the sum of all 11 terms of an A.P. whose 6^th term is 30.2022
• If the first term of an A.P. is 5, the last term is 15 and the sum of first n terms is 30, then find the value of n.2022
• For what value of 'n', are the n ^th terms of the APs: 9, 7, 5,..... and 15,12,9, …. the same?2022
• Find the sum of first 20 terms of an A.P. whose n^th term is given as a_n=5-2 n.2022
• The sum of the first three terms of an A.P. is 33. If the product of first and third term exceeds the second term by 29, find the…2022
• In an A.P., the sum of first n terms is n/2(3 n+5). Find the 25^th term of the A.P.2022
• If the last term of an A.P. of 30 terms is 119 and the 8^th term from the end (towards the first term) is 91, then find the…2022
• In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different…2022

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