What is the general term of the sequence (7,13,19,25,...)?
Answer and explanation
Correct answer: a_n=6n+1
The governing concept is the general term of an arithmetic sequence. The consecutive differences are 13−7=6, 19−13=6, and 25−19=6, so the common difference is 6. For an arithmetic sequence, a_n=a_1+(n−1)d. Substituting a_1=7 and d=6 gives a_n=7+6(n−1)=7+6n−6=6n+1. Therefore option A is correct. Checking n=1 gives 7, n=2 gives 13, and n=4 gives 25, confirming the rule. Option C gives 5 for the first term, option B has an incorrect coefficient and fails at n=2, and option D increases by only 1 rather than by 6.
Frequently asked questions
What is the correct answer to this question?
a_n=6n+1
Why is this the correct answer?
The governing concept is the general term of an arithmetic sequence. The consecutive differences are 13−7=6, 19−13=6, and 25−19=6, so the common difference is 6. For an arithmetic sequence, a_n=a_1+(n−1)d. Substituting a_1=7 and d=6 gives a_n=7+6(n−1)=7+6n−6=6n+1. Therefore option A is correct. Checking n=1 gives 7, n=2 gives 13, and n=4 gives 25, confirming the rule. Option C gives 5 for the first term, option B has an incorrect coefficient and fails at n=2, and option D increases by only 1 rather than by 6.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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