If (a_2=12) and (a_6=32), what is the first term?
Answer and explanation
Correct answer: 7
For an arithmetic progression, \(a_n=a+(n-1)d\). Thus, \(a_2=a+d=12\) and \(a_6=a+5d=32\). Subtracting the equations gives \(4d=20\), so \(d=5\). Substituting \(d=5\) into \(a+d=12\) gives \(a=7\). Therefore, the correct answer is 7. Option 6 may seem close, but it does not satisfy the first-term calculation from \(a+d=12\). Exam tip: when two terms are given, subtract their equations first to find \(d\).
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
For an arithmetic progression, \(a_n=a+(n-1)d\). Thus, \(a_2=a+d=12\) and \(a_6=a+5d=32\). Subtracting the equations gives \(4d=20\), so \(d=5\). Substituting \(d=5\) into \(a+d=12\) gives \(a=7\). Therefore, the correct answer is 7. Option 6 may seem close, but it does not satisfy the first-term calculation from \(a+d=12\). Exam tip: when two terms are given, subtract their equations first to find \(d\).
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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