If (a_2=16) and (a_9=65), what is the first term?
Answer and explanation
Correct answer: 9
For an arithmetic progression, \(a_n=a+(n-1)d\). Thus, \(a_2=a+d=16\) and \(a_9=a+8d=65\). Subtracting the two equations gives \(7d=49\), so \(d=7\). Substituting this into \(a+d=16\) gives \(a=9\). Therefore, the correct answer is 9. Option 8 can result from an incorrect substitution after finding the common difference. Exam tip: form equations for the given terms and subtract them first to find \(d\) quickly.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
For an arithmetic progression, \(a_n=a+(n-1)d\). Thus, \(a_2=a+d=16\) and \(a_9=a+8d=65\). Subtracting the two equations gives \(7d=49\), so \(d=7\). Substituting this into \(a+d=16\) gives \(a=9\). Therefore, the correct answer is 9. Option 8 can result from an incorrect substitution after finding the common difference. Exam tip: form equations for the given terms and subtract them first to find \(d\) quickly.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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