In an AP, the sum of the first and last terms is 150 and the total sum is 1800. Find the number of terms.
Answer and explanation
Correct answer: 24
The governing concept is the AP sum formula written in terms of the first and last terms: Sₙ = n/2 (a + l). The question gives a + l = 150 and Sₙ = 1800. Substitution gives 1800 = n/2 × 150 = 75n. Dividing both sides by 75 gives n = 1800/75 = 24. Thus the AP contains 24 terms, so option D is correct. The common difference is not needed because the sum of the first and last terms is already supplied. The other options would produce totals of 1500, 1650 and 1950 respectively when multiplied by 75, so they do not satisfy the given total of 1800.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
The governing concept is the AP sum formula written in terms of the first and last terms: Sₙ = n/2 (a + l). The question gives a + l = 150 and Sₙ = 1800. Substitution gives 1800 = n/2 × 150 = 75n. Dividing both sides by 75 gives n = 1800/75 = 24. Thus the AP contains 24 terms, so option D is correct. The common difference is not needed because the sum of the first and last terms is already supplied. The other options would produce totals of 1500, 1650 and 1950 respectively when multiplied by 75, so they do not satisfy the given total of 1800.
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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