Sum of n terms in AP
Sum of n terms in AP problems require calculating the total of the first n terms of an arithmetic progression. These problems test your ability to apply AP sum formulas in various contexts.
What You'll Learn
Introduction to Sum of n terms in AP
Sum of n terms in AP problems require calculating the total of the first n terms of an arithmetic progression. These problems test your ability to apply AP sum formulas in various contexts.
Prerequisites
How to Solve Sum of n terms in AP Problems
Step 1: Identify the first term (a) and common difference (d)
Step 2: Identify the number of terms (n)
Step 3: Use formula Sₙ = n/2 × [2a + (n-1)d]
Step 4: Alternatively, if last term (l) is known, use Sₙ = n/2 × (a + l)
Step 5: Substitute values and calculate
Step 6: Simplify to get the sum
Step 7: Verify by adding a few terms manually
Example Problem
Example: Find the sum of first 10 terms of AP: 2, 5, 8, 11, ... Solution: Step 1: a = 2, d = 3, n = 10 Step 2: S₁₀ = 10/2 × [2×2 + (10-1)×3] Step 3: = 5 × [4 + 9×3] Step 4: = 5 × [4 + 27] Step 5: = 5 × 31 = 155 Answer: 155
Pro Tips & Tricks
- Sₙ = n/2 × (first term + last term) - easiest when last term known
- Sₙ = n × (first term + last term)/2 (average of first and last × n)
- For odd n, the middle term × n = sum
- Sum of first n natural numbers: n(n+1)/2
- Sum of first n odd numbers: n²
- Sum of first n even numbers: n(n+1)
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Sum of n terms in AP. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Sum of n terms in AP is an important topic for various competitive exams. Here's how frequently it appears:
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Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: