- A500
- B550
- C575
- D525
Step-by-Step Solution
a + 2d = 600 and a + 6d = 700. Subtracting, 4d = 100 → d = 25. So a = 600 - 2(25) = 550 sets in the first year.
Answer: B) 550
A factory produced 600 sets in its 3rd year and 700 sets in its 7th year. If production increases by the same number of sets every year, how many sets were produced in the 1st year?
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.
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Arithmetic Progressions practice questions
More Class 10 Arithmetic Progressions practice
Digging a well costs ₹250 for the first metre, and every further metre costs ₹75 more…An AP has 25 terms and its middle term is 30. What is the sum of all 25 terms?Ravi sums the first 10 terms of the AP 4, 7, 10, … with n/2[2a + (n - 1)d] and gets 175.…A machine bought for ₹60000 loses ₹4500 of its value every year. What is its value at…The first term of an AP is 3 and the sum of its first 9 terms is 171. Find its common…