Arithmetic Progressions

32 solved questions from Class 10 Mathematics, each with the full working. Tap any question to see the step-by-step solution.

• 1 Ramesh saves money each month in an arithmetic progression. He saves Rs 2000 in the first month and each subsequent month he saves Rs 500 more than the previous month. After how many months will his total savings be at least Rs 1,20,000? Also state the total amount saved at the end of that month. hard 5 marks sum of n terms & inequality
• 2 In an arithmetic progression, the difference between any two successive terms is called the easy MCQ 1 mark definition of AP
• 3 Find the number of terms in an AP whose first term is 3, common difference is 2, and total sum is 255. medium 3 marks finding number of terms from sum
• 4 The first term of an AP is 7 and the common difference is 3. Find its 10^th term. easy 2 marks nth term formula
• 5 The sum of the first 10 terms of an AP is 230. If the first term is 5, what is the common difference? medium MCQ 3 marks sum of n terms
• 6 Find the number of terms in an arithmetic progression whose first term is 5, common difference is 4, and whose total sum of all terms is 230. medium 2 marks finding number of terms from sum
• 7 An arithmetic progression has 9 terms. Its first term is 2 and its last term is 50. Find the sum of the three middle terms. medium 2 marks middle terms of an AP
• 8 What is the sum of the first 5 terms of the arithmetic progression with first term 3 and common difference 4? easy MCQ 1 mark sum of n terms of AP
• 9 Find the 8^th term of the arithmetic progression whose first term is 12 and common difference is -2. easy 1 mark nth term of AP
• 10 In an arithmetic progression, the sum of the first four terms is 54 and the sum of the first seven terms is 147. What is the value of the tenth term? hard MCQ 3 marks finding specific term using given sums
• 11 Find the 5th term of the arithmetic progression whose first term is 3 and common difference is 6. easy MCQ 1 mark nth term of AP
• 12 Ramesh saves money each month in an arithmetic progression. He saves Rs 1500 in the first month and each subsequent month he saves Rs 250 more than the previous month. After how many months will his total savings become at least Rs 2,00,000? Also state the total amount saved at the end of that month. hard 5 marks application of sum of AP to real‑world problem
• 13 In an arithmetic progression, the sum of the first 8 terms is 200 and the sum of the first 4 terms is 80. Find the 8th term. medium 2 marks using two sums to find a term
• 14 Solve the expression: 15 + 25 × 2. medium MCQ BODMAS Rule
• 15 Find the area of a rectangle with length 8 cm and breadth 5 cm. medium MCQ Area of Rectangle
• 16 What is the volume of a cube with edge 3 cm? medium MCQ Volume of Cube
• 17 Find the 10th term of AP: 2, 7, 12, ... medium MCQ Arithmetic Progression
• 18 Distance between points (0,0) and (6,8) is: medium MCQ Distance Formula
• 19 Find surface area of a sphere with radius 7 cm (π = 22/7). medium MCQ Surface Area of Sphere
• 20 If perimeter of a circle is equal to that of a square, find ratio of their areas. medium MCQ Areas Related to Circles
• 21 What is the nth term of an AP with first term a and common difference d? medium MCQ Arithmetic Progression
• 22 Coordinates of midpoint of line joining (x₁, y₁) and (x₂, y₂) is: medium MCQ Midpoint Formula
• 23 Find the value of (2⁰ + 3⁰) × 5⁰. medium MCQ Exponent Laws
• 24 What is the domain, range, or fundamental theorem introduced in 'Arithmetic Progressions' (Class 10 Mathematics)? medium MCQ Functions & Theorems
• 25 What is the derivative or integral formula associated with 'Arithmetic Progressions'? medium MCQ Calculus & Formulae
• 26 How do you find the solution set or optimum value in 'Arithmetic Progressions'? medium MCQ Problem Solving & Optimization
• 27 In an AP, the first term is 4 and the 7th term is 34. What is the common difference? medium MCQ 2 marks finding common difference from two terms
• 28 Find the sum of the first 12 terms of an arithmetic progression with first term 15 and common difference -3. easy 1 mark sum of n terms of AP
• 29 In an arithmetic progression, the sum of the first 8 terms is 320 and the sum of the first 4 terms is 80. Find the common difference. medium 2 marks Determine common difference from sums
• 30 Find the 7th term of the arithmetic progression whose first term is 5 and common difference is 4. easy 1 mark Find nth term of an AP
• 31 Ramesh saves money each month in an arithmetic progression. He saves Rs 1200 in the first month and increases the saving by Rs 300 each subsequent month. After how many months will his total savings be at least Rs 3,00,000? Also state the total amount saved at the end of that month. hard 3 marks Sum of AP to reach a target amount
• 32 An arithmetic progression has 15 terms. The sum of terms from the 3rd to the 10th term inclusive is 200. The first term is 3. What is the common difference? hard MCQ 3 marks Finding common difference from partial sum