If (a_5=27) and (d=5), what is the value of (a_1)?
Answer and explanation
Correct answer: \(7\)
In an arithmetic progression, \(a_n=a_1+(n-1)d\). Therefore, \(a_5=a_1+4d\). Substituting the given values, \(27=a_1+4\times5=a_1+20\), so \(a_1=7\). If \(a_1=9\), the fifth term would be \(29\), not \(27\). Exam tip: there are \(n-1\) common differences between the first term and the \(n\)th term.
Frequently asked questions
What is the correct answer to this question?
\(7\)
Why is this the correct answer?
In an arithmetic progression, \(a_n=a_1+(n-1)d\). Therefore, \(a_5=a_1+4d\). Substituting the given values, \(27=a_1+4\times5=a_1+20\), so \(a_1=7\). If \(a_1=9\), the fifth term would be \(29\), not \(27\). Exam tip: there are \(n-1\) common differences between the first term and the \(n\)th term.
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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