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…
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Key Questions Covered:
- Define an arithmetic progression and state the conditions for a sequence to b…
- Find the 15th term of the AP: 4, 7, 10, 13, ...
- The sum of the first 20 terms of an AP is 650 and the common difference is 3.…
- + 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.