Which is the (n)th term of the sequence (100,90,80,70,\ldots)?
Answer and explanation
Correct answer: (a_n=110-10n)
This is an arithmetic sequence with a negative common difference, because the terms decrease by 10 each time. We have 90−100=−10, 80−90=−10, and 70−80=−10. The nth-term formula for an arithmetic sequence is \\(a_n=a_1+(n-1)d\\). Here, the first term is \\(100\\) and the common difference is \\(−10\\).
Therefore, \\(a_n=100+(n-1)(−10)=100−10n+10=110−10n\\). Hence, option A is correct. Checking the positions makes the result clear: when \\(n=1\\), the expression gives \\(110−10=100\\); when \\(n=2\\), it gives 90; and when \\(n=4\\), it gives 70. The negative sign is essential because the sequence is decreasing. Option B would give 90 at \\(n=1\\), so it cannot represent the sequence.
Frequently asked questions
What is the correct answer to this question?
(a_n=110-10n)
Why is this the correct answer?
This is an arithmetic sequence with a negative common difference, because the terms decrease by 10 each time. We have 90−100=−10, 80−90=−10, and 70−80=−10. The nth-term formula for an arithmetic sequence is \\(a_n=a_1+(n-1)d\\). Here, the first term is \\(100\\) and the common difference is \\(−10\\).
Therefore, \\(a_n=100+(n-1)(−10)=100−10n+10=110−10n\\). Hence, option A is correct. Checking the positions makes the result clear: when \\(n=1\\), the expression gives \\(110−10=100\\); when \\(n=2\\), it gives 90; and when \\(n=4\\), it gives 70. The negative sign is essential because the sequence is decreasing. Option B would give 90 at \\(n=1\\), so it cannot represent the sequence.
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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