Arithmetic Progressions — Class 10 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Arithmetic Progressions" — 9 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Arithmetic Progressions" — 9 important questions with detailed answers for CBSE bo…

By Syllab.in · Updated

Key Questions Covered:

  1. Define an arithmetic progression and state the conditions for a sequence to b…
  2. Find the 15th term of the AP: 4, 7, 10, 13, ...
  3. The sum of the first 20 terms of an AP is 650 and the common difference is 3.…
  4. + 6 more questions in the full chapter

Solutions Summary:

Question Status
Define an arithmetic progression and state the conditions… ✓ Solved
Find the 15th term of the AP: 4, 7, 10, 13, ... ✓ Solved
The sum of the first 20 terms of an AP is 650 and the com… ✓ Solved

Showing 3 of 9 questions

Q1: Define an arithmetic progression and state the conditions for a sequence to be an AP.

Arithmetic Progression (AP): An arithmetic progression is a sequence of numbers where the difference between any two consecutive terms is constant. General form: a, a + d, a + 2d, a + 3d, ... where a = first term d = common difference (constant) Condition for AP: A sequence with terms t₁, t...

Q2: Find the 15th term of the AP: 4, 7, 10, 13, ...

Given AP: 4, 7, 10, 13, ... Step 1: Identify the parameters First term: a = 4 Common difference: d = 7 - 4 = 3 (Verify: 10 - 7 = 3, 13 - 10 = 3 ✓) We need to find the 15th term, so n = 15. Step 2: Use the formula for nth term tₙ = a + (n - 1)d t₁₅ = 4 + (15 - 1) × 3 t₁₅ = 4 + 14 × 3 t₁₅ = 4 + 42 ...

Q3: The sum of the first 20 terms of an AP is 650 and the common difference is 3. Find the first term.

Given: Sum of first 20 terms: S₂₀ = 650 Common difference: d = 3 Number of terms: n = 20 Find: First term a = ? Step 1: Use the sum formula for AP Sₙ = n/2 × (2a + (n - 1)d) Substitute the known values: 650 = 20/2 × (2a + (20 - 1) × 3) 650 = 10 × (2a + 19 × 3) 650 = 10 × (2a + 57) Step 2: Solve f...

Showing 3 of 9 questions. Visit the full page for complete solutions.