Which is the (n)th term of the sequence (13,17,21,25,\ldots)?
Answer and explanation
Correct answer: (a_n=4n+9)
This is an arithmetic sequence because every term increases by the same amount. The common difference is 4: 17−13=4, 21−17=4, and 25−21=4. For an arithmetic sequence, the nth term is found by starting with the first term and adding the common difference \\(n-1\\) times. Thus, \\(a_n=a_1+(n-1)d\\), where \\(a_1=13\\) and \\(d=4\\).
Substitution gives \\(a_n=13+(n-1)4=13+4n-4=4n+9\\). Therefore, option A is correct. A quick check confirms it: for \\(n=1\\), the formula gives \\(4(1)+9=13\\); for \\(n=2\\), it gives 17; and for \\(n=4\\), it gives 25. The other expressions do not produce the given first terms in the required order.
Frequently asked questions
What is the correct answer to this question?
(a_n=4n+9)
Why is this the correct answer?
This is an arithmetic sequence because every term increases by the same amount. The common difference is 4: 17−13=4, 21−17=4, and 25−21=4. For an arithmetic sequence, the nth term is found by starting with the first term and adding the common difference \\(n-1\\) times. Thus, \\(a_n=a_1+(n-1)d\\), where \\(a_1=13\\) and \\(d=4\\).
Substitution gives \\(a_n=13+(n-1)4=13+4n-4=4n+9\\). Therefore, option A is correct. A quick check confirms it: for \\(n=1\\), the formula gives \\(4(1)+9=13\\); for \\(n=2\\), it gives 17; and for \\(n=4\\), it gives 25. The other expressions do not produce the given first terms in the required order.
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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