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Arithmetic Progressions Class 10 Maths Worksheet with Answers Chapter 5

Updated:9 Mins Read

Try solving the worksheet questions only after completing the chapter. This worksheet is going to help you in “spotting an Arithmetic Progressions” to solving full, exam-style applications without much of panic. The entire worksheet is organised into four parts: Basic, Standard, Advance, and HOTS. Do it in order as it is given in the worksheet, keep your steps clean, and use the hints only after you’ve tried sincerely. The primary topics covered in the chapter –

  • Arithmetic progression meaning
  • Common difference concept
  • nᵗʰ term formula
  • Sum of terms
  • AP word problems

Class 10 Maths Worksheet – Chapter 5: Arithmetic Progressions

Basic

  1. Write the meaning of Arithmetic Progression (AP) in one line.
  2. For the list 12, 15, 18, 21, … find:

    • First term (a)
    • Common difference (d)
  3. Find the next two terms:
    4, 10, 16, 22, …
  4. Check whether it is an AP (Yes/No). If Yes, write d:
    −3, −1, 1, 3, …
  5. Check whether it is an AP (Yes/No):
    1, 1, 2, 3, 5, 8, …
  6. Write the general form of an AP using a and d (up to 5 terms).
  7. If a = 7 and d = 3, write the first four terms of the AP.

Standard

  1. Find the 10th term of the AP:
    2, 7, 12, …
  2. Which term of the AP 21, 18, 15, … is −81?
  3. Find whether 301 is a term of the AP:
    5, 11, 17, 23, …
    (If yes, find its position; if no, write why.)
  4. How many two-digit numbers are divisible by 3?
    (Hint: 12, 15, 18, …, 99 forms an AP.)
  5. Find n if:
    a = 7, d = 3, and aₙ = 205
  6. Find the 11th term from the end (towards the first term) of:
    10, 7, 4, …, −62
  7. Fill the missing term to make it an AP:
    5, __, 13

Advance

  1. Shakila puts ₹100 in a box on her daughter’s 1st birthday and increases it by ₹50 every year.
    Find the total amount collected by the 21st birthday.
  2. Find the sum of the first 22 terms of the AP:
    8, 3, −2, …
  3. Find the number of terms in the AP:
    7, 13, 19, …, 205
  4. The sum of first 14 terms of an AP is 1050 and the first term is 10.
    Find the common difference (d), then find the 20th term.
  5. How many terms of the AP 24, 21, 18, … must be taken so that the sum is 78?
    (More than one answer may be possible.)
  6. The first term is 5, last term is 45, and the sum is 400.
    Find the number of terms (n) and the common difference (d).
  7. A contract penalty is ₹200 for the 1st day, ₹250 for the 2nd day, ₹300 for the 3rd day, …
    Find the total penalty for 30 days of delay.

HOTS

  1. Without listing all terms, decide whether these form an AP. If yes, write d:

    • 0.2, 0.22, 0.222, 0.2222, …
    • 3, 3 + √2, 3 + 2√2, 3 + 3√2, …
  2. If the 17th term exceeds the 10th term by 7, find the common difference d.
  3. Two APs have the same common difference.
    The difference between their 100th terms is 100.
    What is the difference between their 1000th terms?
  4. If the sum of first n terms of an AP is Sₙ = 4n − n²,
    find:

    • S₁
    • first term a
    • second term a₂
  5. A spiral is made of semicircles with radii 0.5 cm, 1.0 cm, 1.5 cm, … (13 semicircles).
    Find total length of the spiral.
    (Use π = 22/7; length of a semicircle = πr.)
  6. 200 logs are stacked as: 20 in bottom row, 19 in next, 18 in next, …
    Find:

    • Number of rows
    • Logs in top row
  7. Potato race: first potato is 5 m from bucket, next potatoes are 3 m apart, total 10 potatoes.
    A competitor runs to each potato and back to bucket each time.
    Find total distance run.

Answer Key

Basic – Answers

  1. Ans: An AP is a list of numbers where each term is obtained by adding a fixed number to the previous term.
    Hint: That fixed number is the common difference d.
  2. Ans: a = 12, d = 3
    Hint: d = 15 − 12 = 3.
  3. Ans: 28, 34
    Hint: Add d = 6 each time.
  4. Ans: Yes, d = 2
    Hint: −1 − (−3) = 2, 1 − (−1) = 2.
  5. Ans: No
    Hint: Differences are not constant (1−1=0, 2−1=1, 3−2=1, 5−3=2…).
  6. Ans: a, a + d, a + 2d, a + 3d, a + 4d, …
    Hint: Each step adds the same d.
  7. Ans: 7, 10, 13, 16
    Hint: Start at a, add d repeatedly.

Standard – Answers

  1. Ans: a = 2, d = 5 ⇒ a₁₀ = a + 9d = 2 + 9×5 = 47
    Hint: Use aₙ = a + (n − 1)d.
  2. Ans: a = 21, d = −3
    −81 = 21 + (n − 1)(−3)
    −81 = 24 − 3n ⇒ n = 35
    Hint: Solve for n carefully.
  3. Ans: a = 5, d = 6
    301 = 5 + (n − 1)6 ⇒ 301 = 6n − 1 ⇒ n = 302/6 = 151/3 (not an integer)
    So, 301 is not a term.
    Hint: n must be a positive integer.
  4. Ans: Terms: 12 to 99 with d = 3
    99 = 12 + (n − 1)3 ⇒ 87 = 3(n − 1) ⇒ n − 1 = 29 ⇒ n = 30
    Hint: Count terms using aₙ formula.
  5. Ans: 205 = 7 + (n − 1)3 ⇒ 198 = 3(n − 1) ⇒ n − 1 = 66 ⇒ n = 67
    Hint: Isolate (n − 1).
  6. Ans: First find total terms:
    −62 = 10 + (n − 1)(−3) ⇒ −72 = −3(n − 1) ⇒ n − 1 = 24 ⇒ n = 25
    11th from last = (25 − 11 + 1)th = 15th term
    a₁₅ = 10 + 14(−3) = 10 − 42 = −32
    Hint: “kth from last” = (n − k + 1)th from start.
  7. Ans: 5, 9, 13 (d = 4)
    Hint: Middle term is average: (5 + 13)/2 = 9.

Advance – Answers

  1. Ans: AP: 100, 150, 200, … with a = 100, d = 50, n = 21
    S₂₁ = 21/2[2×100 + 20×50] = 21/2[200 + 1000] = 21/2 × 1200 = 12600
    Hint: Use Sₙ = n/2[2a + (n − 1)d].
  2. Ans: a = 8, d = −5, n = 22
    S₂₂ = 22/2[2×8 + 21(−5)] = 11[16 − 105] = 11(−89) = −979
    Hint: Put values neatly before multiplying.
  3. Ans: a = 7, d = 6, last term l = 205
    205 = 7 + (n − 1)6 ⇒ 198 = 6(n − 1) ⇒ n − 1 = 33 ⇒ n = 34
    Hint: Last term is aₙ.
  4. Ans: S₁₄ = 1050, a = 10
    1050 = 14/2[2×10 + 13d] = 7(20 + 13d)
    150 = 20 + 13d ⇒ 13d = 130 ⇒ d = 10
    a₂₀ = 10 + 19×10 = 200
    Hint: First solve d, then use aₙ.
  5. Ans: a = 24, d = −3
    78 = n/2[48 + (n − 1)(−3)] = n/2[51 − 3n]
    156 = 51n − 3n² ⇒ 3n² − 51n + 156 = 0
    n² − 17n + 52 = 0 ⇒ (n − 4)(n − 13) = 0
    So n = 4 or 13
    Hint: Two answers can happen when later terms cancel earlier terms.
  6. Ans: S = n/2(a + l)
    400 = n/2(5 + 45) = n/2 × 50 = 25n ⇒ n = 16
    d = (l − a)/(n − 1) = (45 − 5)/15 = 40/15 = 8/3
    Hint: Use Sₙ = n/2(a + l) when d is unknown.
  7. Ans: AP: 200, 250, 300, … with a = 200, d = 50, n = 30
    S₃₀ = 30/2[2×200 + 29×50] = 15[400 + 1450] = 15×1850 = 27750
    Hint: Total penalty = sum of AP.

HOTS – Answers

  1. Ans:

    • 0.2, 0.22, 0.222, … is not an AP (differences keep changing).
    • 3, 3 + √2, 3 + 2√2, … is an AP with d = √2.

    Hint: Constant difference is the only test.

  2. Ans: a₁₇ − a₁₀ = [a + 16d] − [a + 9d] = 7d = 7 ⇒ d = 1
    Hint: Subtract terms; a cancels.
  3. Ans: Difference between nth terms of two APs with same d is constant.
    So difference between 1000th terms is also 100.
    Hint: Same d means “gap” never changes.
  4. Ans: S₁ = 4(1) − 1² = 3 ⇒ a = 3
    S₂ = 4(2) − 2² = 4
    a₂ = S₂ − S₁ = 4 − 3 = 1
    Hint: aₙ = Sₙ − Sₙ₋₁.
  5. Ans: Total length = π(r₁ + r₂ + … + r₁₃)
    Radii form AP: 0.5, 1.0, 1.5, …, 6.5 (13 terms)
    Sum of radii = 13/2(0.5 + 6.5) = 13/2 × 7 = 45.5
    Length = π × 45.5 = (22/7)×45.5 = 143
    Hint: Semicircle length = πr (not 2πr).
  6. Ans: Rows are 20, 19, 18, …, k
    Number of rows = n, last row has k = 20 − (n − 1)
    Sum: 200 = n/2(20 + k) = n/2(20 + 21 − n) = n/2(41 − n)
    So 400 = n(41 − n) ⇒ n² − 41n + 400 = 0 ⇒ (n − 16)(n − 25) = 0
    Valid: n = 16 (since top row must be positive)
    Top row k = 20 − 15 = 5
    Hint: Reject n = 25 because it gives k ≤ 0.
  7. Ans: Distances to potatoes from bucket: 5, 8, 11, … (10 terms, d = 3)
    Total run = 2 × (5 + 8 + 11 + … up to 10 terms)
    Sum = S₁₀ = 10/2[2×5 + 9×3] = 5[10 + 27] = 185
    Total run = 2×185 = 370 m
    Hint: Each potato trip is “go + return”, so multiply by 2.

Worksheet for Other chapters

Amit, a BE in Mechanical Engineering, is a math enthusiast dedicated to making math fun and accessible for kids in classes 1 to 10. With a knack for simplifying complex concepts, Amit offers easy-to-understand solutions, fostering a love for math in young minds across India.

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