In a test, the value is 1250 units at the first stage and decreases by 55 units at each next stage. At which stage will the value be 260 units?
Answer and explanation
Correct answer: 19वाँ
This is an arithmetic-progression word problem. The first-stage value is a₁ = 1250, and because the value decreases by 55 at every step, the common difference is d = −55. The nth-stage value is therefore aₙ = a₁ + (n − 1)d = 1250 − 55(n − 1). Set this equal to 260: 1250 − 55(n − 1) = 260. Thus 55(n − 1) = 990, so n − 1 = 18 and n = 19. A check gives 1250 − 18 × 55 = 1250 − 990 = 260. Therefore, the value is 260 units at the 19th stage, making option C correct. The negative sign in the common difference is essential because the sequence is decreasing.
Frequently asked questions
What is the correct answer to this question?
19वाँ
Why is this the correct answer?
This is an arithmetic-progression word problem. The first-stage value is a₁ = 1250, and because the value decreases by 55 at every step, the common difference is d = −55. The nth-stage value is therefore aₙ = a₁ + (n − 1)d = 1250 − 55(n − 1). Set this equal to 260: 1250 − 55(n − 1) = 260. Thus 55(n − 1) = 990, so n − 1 = 18 and n = 19. A check gives 1250 − 18 × 55 = 1250 − 990 = 260. Therefore, the value is 260 units at the 19th stage, making option C correct. The negative sign in the common difference is essential because the sequence is decreasing.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Word problems based on APs.
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