Example 1 · level 1
Find the sum of the first 7 terms of the AP 13, 18, 23, …
Show solution
- S7 = 7/2 × [26 + 6 × 5]
- = 7/2 × 56
- = 196.
Answer: 196
CLASS 10 MATHS · ARITHMETIC PROGRESSIONS
Arithmetic progression: sum of n terms
Sₙ = n/2 × [2a + (n − 1)d], or Sₙ = n/2 × (first term + last term).
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Worked examples
Example 2 · level 2
Harpreet saves ₹250 in the first month and ₹50 more each month than the month before. How much is saved in total in 24 months?
Show solution
- Last month's saving = 250 + 23 × 50 = ₹1400.
- Total = 24/2 × (250 + 1400) = ₹19,800.
Answer: ₹19,800
Example 3 · level 3
How many terms of the AP 13, 15, 17, … must be added to get a sum of 85?
Show solution
- n/2 × [26 + (n − 1)2] = 85
- 2n² + 24n − 170 = 0
- The positive solution is n = 5.
Answer: 5