If a_1 = 17 and each next term is 9 less than the previous term, what is the explicit rule?
Answer and explanation
Correct answer: a_n = 26 - 9n
The governing concept is the explicit formula for an arithmetic sequence: a_n = a_1 + (n - 1)d. Here the first term is a_1 = 17, and each term is 9 less than the preceding one, so the common difference is d = -9. Substitution gives a_n = 17 + (n - 1)(-9) = 17 - 9n + 9 = 26 - 9n. Checking n = 1 gives 26 - 9 = 17, and n = 2 gives 26 - 18 = 8, which is indeed 9 less. Option A gives 8 at n = 1, because it forgets the n - 1 adjustment. Option C increases rather than decreases, and D also has the wrong direction. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
a_n = 26 - 9n
Why is this the correct answer?
The governing concept is the explicit formula for an arithmetic sequence: a_n = a_1 + (n - 1)d. Here the first term is a_1 = 17, and each term is 9 less than the preceding one, so the common difference is d = -9. Substitution gives a_n = 17 + (n - 1)(-9) = 17 - 9n + 9 = 26 - 9n. Checking n = 1 gives 26 - 9 = 17, and n = 2 gives 26 - 18 = 8, which is indeed 9 less. Option A gives 8 at n = 1, because it forgets the n - 1 adjustment. Option C increases rather than decreases, and D also has the wrong direction. Thus option B is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
