- A510
- B1020
- C460
- D560
Step-by-Step Solution
. S₁₅ = seats.
Answer: A) 510
Find the total number of seats in the first 15 rows of the stadium where the first row has 20 seats and each successive row has 2 more seats.
Class 10Arithmetic ProgressionsAlgebra — Sequences
Key idea: Common AP word problems
**Salaries**: 'Person earns ₹X in year 1 with annual increase of ₹Y. Find salary in year n / total over n years.' → AP with a = X, d = Y.
**Stadium seating**: 'Front row has 30 seats; each row 4 more. 25 rows. Total seats?' → AP with a = 30, d = 4. S₂₅ = ?
**Loans/installments**: equal monthly payments form an AP.
**Number patterns**: 'Multiples of 5 between 100 and 500: how many? Sum?' → AP with a = 100, d = 5, last = 500.
Always identify a, d, and what's asked (term aₙ or sum Sₙ). Check whether n is the COUNT or the POSITION.
**Stadium seating**: 'Front row has 30 seats; each row 4 more. 25 rows. Total seats?' → AP with a = 30, d = 4. S₂₅ = ?
**Loans/installments**: equal monthly payments form an AP.
**Number patterns**: 'Multiples of 5 between 100 and 500: how many? Sum?' → AP with a = 100, d = 5, last = 500.
Always identify a, d, and what's asked (term aₙ or sum Sₙ). Check whether n is the COUNT or the POSITION.
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