Sequences and Series — Class 11 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Sequences and Series" — 8 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Sequences and Series" — 8 important questions with detailed answers for CBSE board…

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Key Questions Covered:

  1. Find the 15th term of the arithmetic progression (AP) 2, 5, 8, 11, ...
  2. The sum of first n terms of an AP is Sₙ = n²/2 + 3n/2. Find the AP and its 20…
  3. Find the sum of the first 20 terms of the geometric progression (GP) 3, 6, 12…
  4. + 5 more questions in the full chapter

Solutions Summary:

Question Status
Find the 15th term of the arithmetic progression (AP) 2, … ✓ Solved
The sum of first n terms of an AP is Sₙ = n²/2 + 3n/2. Fi… ✓ Solved
Find the sum of the first 20 terms of the geometric progr… ✓ Solved

Showing 3 of 8 questions

Q1: Find the 15th term of the arithmetic progression (AP) 2, 5, 8, 11, ...

Given AP: 2, 5, 8, 11, ... First term a = 2 Common difference d = 5 - 2 = 3 Step 1: Use the formula for nth term of an AP: aₙ = a + (n - 1)d Step 2: Substitute n = 15, a = 2, d = 3: a₁₅ = 2 + (15 - 1) × 3 a₁₅ = 2 + 14 × 3 a₁₅ = 2 + 42 a₁₅ = 44 Final Answer: The 15th term is 44

Q2: The sum of first n terms of an AP is Sₙ = n²/2 + 3n/2. Find the AP and its 20th term.

Given: Sₙ = n²/2 + 3n/2 Step 1: Find the first term a₁ using S₁: S₁ = (1)²/2 + 3(1)/2 = 1/2 + 3/2 = 2 So a₁ = 2 Step 2: Find a₂ using S₂: S₂ = (2)²/2 + 3(2)/2 = 2 + 3 = 5 So a₁ + a₂ = 5 Therefore a₂ = 5 - 2 = 3 Step 3: Find common difference d: d = a₂ - a₁ = 3 - 2 = 1 Step 4: Verify with a₃: S₃ ...

Q3: Find the sum of the first 20 terms of the geometric progression (GP) 3, 6, 12, 24, ...

Given GP: 3, 6, 12, 24, ... First term a = 3 Common ratio r = 6/3 = 2 Step 1: Use the formula for sum of n terms of a GP (r ≠ 1): Sₙ = a(rⁿ - 1)/(r - 1) Step 2: Substitute n = 20, a = 3, r = 2: S₂₀ = 3(2²⁰ - 1)/(2 - 1) S₂₀ = 3(2²⁰ - 1)/1 S₂₀ = 3(1048576 - 1) S₂₀ = 3 × 1048575 S₂₀ = 3145725 Final ...

Showing 3 of 8 questions. Visit the full page for complete solutions.