If (a_7=52) and (d=7), what is the value of (a_1)?
Answer and explanation
Correct answer: 10
In an arithmetic progression, \(a_n=a_1+(n-1)d\). Hence, \(a_7=a_1+6d\). Substituting the given values, \(52=a_1+6\times7=a_1+42\), so \(a_1=10\). If 12 were used, the seventh term would be \(12+42=54\), not 52. Exam tip: the number of common differences before the \(n\)th term is always \(n-1\).
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
In an arithmetic progression, \(a_n=a_1+(n-1)d\). Hence, \(a_7=a_1+6d\). Substituting the given values, \(52=a_1+6\times7=a_1+42\), so \(a_1=10\). If 12 were used, the seventh term would be \(12+42=54\), not 52. Exam tip: the number of common differences before the \(n\)th term is always \(n-1\).
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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