In an experiment, the temperature is 760 units at the first stage and decreases by 32 units at each next stage. At which stage will it be 280 units?
Answer and explanation
Correct answer: 16th
The stage temperatures form an arithmetic progression with first term a=760 and common difference d=−32, because the temperature decreases by 32 at every step. The nth-stage temperature is therefore a_n=760+(n−1)(−32). Set this equal to 280: 760−32(n−1)=280, so 32(n−1)=480, n−1=15, and n=16. Thus the temperature reaches 280 units at the 16th stage, making option C correct. The negative sign is essential; using +32 would describe an increasing sequence. The neighboring choices arise from shifting the stage count by one.
Frequently asked questions
What is the correct answer to this question?
16th
Why is this the correct answer?
The stage temperatures form an arithmetic progression with first term a=760 and common difference d=−32, because the temperature decreases by 32 at every step. The nth-stage temperature is therefore a_n=760+(n−1)(−32). Set this equal to 280: 760−32(n−1)=280, so 32(n−1)=480, n−1=15, and n=16. Thus the temperature reaches 280 units at the 16th stage, making option C correct. The negative sign is essential; using +32 would describe an increasing sequence. The neighboring choices arise from shifting the stage count by one.
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.
