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: 19th
This is an arithmetic-progression word problem. The first-stage value is a₁ = 1250, and a decrease of 55 at every next stage means the common difference is d = −55. Thus the value at stage n is aₙ = a₁ + (n − 1)d = 1250 − 55(n − 1). Set this equal to 260: 1250 − 55(n − 1) = 260. Rearranging gives 55(n − 1) = 990, so n − 1 = 18 and n = 19. Checking directly, after 18 decreases the value is 1250 − 18 × 55 = 1250 − 990 = 260. Therefore the value is 260 at the 19th stage, so option C is correct. The negative common difference is essential because the sequence decreases.
Frequently asked questions
What is the correct answer to this question?
19th
Why is this the correct answer?
This is an arithmetic-progression word problem. The first-stage value is a₁ = 1250, and a decrease of 55 at every next stage means the common difference is d = −55. Thus the value at stage n is aₙ = a₁ + (n − 1)d = 1250 − 55(n − 1). Set this equal to 260: 1250 − 55(n − 1) = 260. Rearranging gives 55(n − 1) = 990, so n − 1 = 18 and n = 19. Checking directly, after 18 decreases the value is 1250 − 18 × 55 = 1250 − 990 = 260. Therefore the value is 260 at the 19th stage, so option C is correct. The negative common difference is essential because the sequence decreases.
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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