- A350 cm
- B770 cm
- C275 cm
- D385 cm
Step-by-Step Solution
2.5 m = 250 cm and 250 ÷ 25 = 10 gaps, so there are 11 rungs. Their lengths form an AP with , so the wood needed is cm. Counting 10 rungs instead of 11 gives 350 cm.
Answer: D) 385 cm
A ladder has rungs 25 cm apart, and the rungs shorten uniformly from 45 cm at the bottom to 25 cm at the top. The top and bottom rungs are 2.5 m apart. What total length of wood is needed for the rungs?
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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