What is the 40th term of the sequence (15, 24, 33, 42, ...)?
Answer and explanation
Correct answer: 366
The governing concept is the nth-term formula for an arithmetic sequence. The first term is a_1 = 15, and the common difference is d = 9 because 24 − 15 = 9 and 33 − 24 = 9. Hence a_n = a_1 + (n − 1)d = 15 + 9(n − 1) = 9n + 6. Substituting n = 40 gives a_40 = 9(40) + 6 = 360 + 6 = 366. The same result comes from noting that there are 39 intervals from the first term to the fortieth term: 15 + 39 × 9 = 15 + 351 = 366. Therefore, option B is correct. Option A is one difference too small, option C is one difference too large, and option D is two differences too large. The n − 1 factor is essential because the first term already has index 1.
Frequently asked questions
What is the correct answer to this question?
366
Why is this the correct answer?
The governing concept is the nth-term formula for an arithmetic sequence. The first term is a_1 = 15, and the common difference is d = 9 because 24 − 15 = 9 and 33 − 24 = 9. Hence a_n = a_1 + (n − 1)d = 15 + 9(n − 1) = 9n + 6. Substituting n = 40 gives a_40 = 9(40) + 6 = 360 + 6 = 366. The same result comes from noting that there are 39 intervals from the first term to the fortieth term: 15 + 39 × 9 = 15 + 351 = 366. Therefore, option B is correct. Option A is one difference too small, option C is one difference too large, and option D is two differences too large. The n − 1 factor is essential because the first term already has index 1.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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