How to Solve Arithmetic Progressions — Step by Step Guide
Find the nth term, sum of n terms and common difference of APs. This guide covers Class 10 to 10.
Step-by-Step Method
- 1
Identify the first term (a) and common difference (d) = a₂ - a₁.
- 2
nth term: aₙ = a + (n-1)d.
- 3
Sum of first n terms: Sₙ = n/2 × [2a + (n-1)d] or Sₙ = n/2 × (a + l) where l is the last term.
- 4
To find how many terms: set aₙ equal to the given value and solve for n.
- 5
If three numbers are in AP, the middle number is the average of the other two.
Worked Example
Problem: Find the 10th term and sum of first 10 terms of AP: 3, 7, 11, 15, ...
Solution: a = 3, d = 4. a₁₀ = 3 + 9(4) = 39. S₁₀ = 10/2 × (3 + 39) = 5 × 42 = 210.
Common Mistakes to Avoid
- ✗
Using n instead of (n-1) in the nth term formula.
- ✗
Confusing the nth term formula with the sum formula.
- ✗
Not checking whether the common difference is positive or negative.
- ✗
Assuming the first term is always 1.
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Frequently Asked Questions
- How do I solve Arithmetic Progressions problems?
- Identify the first term (a) and common difference (d) = a₂ - a₁. nth term: aₙ = a + (n-1)d.
- What are common mistakes in Arithmetic Progressions?
- Using n instead of (n-1) in the nth term formula. Confusing the nth term formula with the sum formula.
- Which class covers Arithmetic Progressions?
- Arithmetic Progressions is typically taught in Class 10. SparkEd has free practice for all these grades.
- Where can I practise Arithmetic Progressions for free?
- SparkEd offers free chapter-wise practice for Arithmetic Progressions aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.
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