If the nth term of a sequence is \(a_n=6n-5\), what will be the 18th term?
Answer and explanation
Correct answer: 103
The governing concept is evaluation of an explicit nth-term rule. Since \(a_n=6n-5\), substitute the requested index \(n=18\) directly into the formula: \(a_{18}=6(18)-5=108-5=103\). Therefore option B is correct. No recursive calculation or summation is needed because the formula already gives any term directly from its position. Option A would result from subtracting 7 instead of 5, option C from an arithmetic error after multiplication, and option D from subtracting 1 rather than 5. The sequence has common difference 6, which is consistent with this linear rule.
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What is the correct answer to this question?
103
Why is this the correct answer?
The governing concept is evaluation of an explicit nth-term rule. Since \(a_n=6n-5\), substitute the requested index \(n=18\) directly into the formula: \(a_{18}=6(18)-5=108-5=103\). Therefore option B is correct. No recursive calculation or summation is needed because the formula already gives any term directly from its position. Option A would result from subtracting 7 instead of 5, option C from an arithmetic error after multiplication, and option D from subtracting 1 rather than 5. The sequence has common difference 6, which is consistent with this linear rule.
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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