A factory produces 120, 135, 150, ... items per day. What is the total production in 10 days?
Answer and explanation
Correct answer: 1875
The daily production forms an arithmetic progression because the increase from one day to the next is constant: d = 135 − 120 = 15. Here the first term is a = 120 and the number of days is n = 10. Using S_n = n/2[2a + (n − 1)d], we get S_10 = 10/2[2(120) + 9(15)] = 5[240 + 135] = 5 × 375 = 1875 items. Hence option A is correct. The other values do not result from applying the AP sum formula; simply multiplying the first or last daily production by ten would also be incorrect because production changes each day.
Frequently asked questions
What is the correct answer to this question?
1875
Why is this the correct answer?
The daily production forms an arithmetic progression because the increase from one day to the next is constant: d = 135 − 120 = 15. Here the first term is a = 120 and the number of days is n = 10. Using S_n = n/2[2a + (n − 1)d], we get S_10 = 10/2[2(120) + 9(15)] = 5[240 + 135] = 5 × 375 = 1875 items. Hence option A is correct. The other values do not result from applying the AP sum formula; simply multiplying the first or last daily production by ten would also be incorrect because production changes each day.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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