Class 10 Arithmetic Progressions Previous Year Questions

    Q1:

    If the sum of the first 14 terms of an A.P. is 1050 and the first term is 10, then find the 20th term and the nth term.

    CBSE [2024]

    Easy

    Q2:

    The first term of an A.P. is 5, the last term is 45 and the sum of all the terms is 400. Find the number of terms and the common difference of the A.P.

    CBSE [2024]

    Easy

    Q3:

    Find the next term of the A.P √18, √50, √98, ...

    CBSE [2024]

    Easy

    Q4:

    Question Image

    Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/number/maps to discover hidden treasures. Players engage in a thrilling quest, solving puzzles and riddles to unveil the location of the coveted prize. While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forming an A.P. If the number on the nᵗʰ spot is 20 + 4n, then answer the following questions to help the players in spotting the clues: (i) Which number is on first spot? (ii) (a) Which spot is numbered as 112? OR (b) What is the sum of all the numbers on the first 10 spots? (iii) Which number is on the (n - 2)ᵗʰ spot?

    CBSE [2024]

    Easy

    Q5:

    The ratio of the 10ᵗʰ term to its 30ᵗʰ term of an A.P is 1:3 and the sum of its first six terms is 42. Find the first term and the common difference of A.P.

    CBSE [2024]

    Medium

    Q6:

    Find the common difference of the A.P: \(\frac{1}{2x}\), \(\frac{1 - 4x}{2x}\), \(\frac{1 - 8x}{2x}\), .....

    CBSE [2024]

    Easy

    Q7:

    Question Image

    250 logs are stacked in the following manner: 22 logs in the bottom row, 21 in the next row, 20 in the row next to it and so on. In how many rows, are the 250 logs placed and how many logs are there in the top row?

    CBSE [2023]

    Medium

    Q8:

    The ratio of the 11ᵗʰ term to 17ᵗʰ term of an A.P is 3 : 4. Find the ratio of 5ᵗʰ term to 21ˢᵗ term of the same A.P. Also, find the ratio of the sum of first 5 terms to that of first 21 terms.

    CBSE [2023]

    Hard

    Q9:

    In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures. One such pattern is shown below. Observe the pattern and answer the following questions using Arithmetic Progression : (a) Write the AP for the number of triangles used in the figures. Also, write the nth term of this AP. (b) Which figure has 61 matchsticks

    CBSE [2022]

    Medium

    Q10:

    If pᵗʰ term of an A.P. is q and qᵗʰ term is p, then prove that its nᵗʰ term is (p + q - n).

    CBSE [2023]

    Hard

    Q11:

    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) terms is zero.

    CBSE [2024]

    Hard

    Q12:

    In an A.P of 40 terms, the sum of first 9 terms is 153 and the sum of last 6 terms is 687. Determine the first term and common difference of A.P. Also, find the sum of all the terms of the A.P.

    CBSE [2024]

    Hard

    Q13:

    The sum of first and 8ᵗʰ terms of an A.P is 32 and their product is 60. Find the first term and common difference of the A.P. Hence, also find the sum of its first 20 terms.

    CBSE [2024]

    Hard

    Q14:

    How many terms of the arithmetic progression 45, 39, 33, .... must be taken so that their sum is 180? Explain the double answer.

    CBSE [2023]

    Medium

    Q15:

    Find the next term of the A.P: √6, √24, √54, .....

    CBSE [2023]

    Easy

    Q16:

    Assertion (A): a, b, c are in A.P. if and only if 2b = a + c. Reason (R): The sum of first n odd natural numbers is n². (a) Both Assertion(A) and Reason(R) are true and Reason(R) is the correct explanation of Assertion(A). (b) Both Assertion(A) and Reason(R) are true and Reason(R) is not the correct explanation of Assertion(A). (c) Assertion (A) is true but Reason (R) is false. (d) Assertion (A) is false but Reason (R) is true.

    CBSE [2023]

    Easy

    Q17:

    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?

    CBSE [2023]

    Easy

    Q18:

    Which term of the A.P. : 65, 61, 57, 53, ...... is the first negative term?

    CBSE [2023]

    Hard

    Q19:

    If the sum of first 6 terms of an A.P is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

    CBSE [2023]

    Medium

    Q20:

    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 A.P.

    CBSE [2022]

    Hard

    Q21:

    If the last term of an A.P of 30 terms is 119 and the 8ᵗʰ term from the end is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.

    CBSE [2022]

    Hard

    Q22:

    How many natural numbers are there between 1 and 1000 which are divisible by 5 but not by 2?

    CBSE [2022]

    Medium

    Q23:

    For what value of 'n' are the nᵗʰ terms of the APs: 9, 7, 5, .... and 15, 12, 9, .... the same?

    CBSE [2022]

    Medium

    Q24:

    Find the sum of first 20 terms of an A.P whose nᵗʰ term is given as aₙ = 5 - 2n

    CBSE [2022]

    Easy

    Q25:

    Which term of the A.P \(-\frac{11}{2}\), -3, \(-\frac{1}{2}\), .... is \(\frac{49}{2}\)?

    CBSE [2022]

    Easy