Example 1 · level 1
Find the 15th term of the AP 6, 8, 10, …
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- d = 2.
- a15 = 6 + 14 × 2 = 34.
Answer: 34
CLASS 11 MATHS · SEQUENCES AND SERIES
AP and GP: nth term and sum
AP: aₙ = a + (n − 1)d, Sₙ = n/2 [2a + (n − 1)d]. GP: aₙ = arⁿ⁻¹, Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1.
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Worked examples
Example 2 · level 2
A startup in Guwahati pays a trainee ₹10,000 in month 1 and raises the stipend by ₹2,500 every month. What is the total paid over 12 months (in ₹)?
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- S = 12/2 × 47,500 = ₹2,85,000.
Answer: ₹2,85,000
Example 3 · level 3
Meera saves ₹1 in week 1 and doubles the amount every week. How much is saved in total over 8 weeks (in ₹)?
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- S8 = 1(256 − 1)/(2 − 1) = 255.
Answer: ₹255