In the sequence (75,68,61,54,\ldots), how many terms are positive?
Answer and explanation
Correct answer: 11
This is an arithmetic progression with first term \(a=75\) and common difference \(d=-7\). Its \(n\)th term is \(a_n=75-7(n-1)\). For a term to be positive, \(75-7(n-1)>0\), which gives \(n<\frac{82}{7}\approx11.71\). Hence, the greatest integral value of \(n\) is 11, so 11 terms are positive. The 12th term is \(75-7\times11=-2\), so 12 terms cannot be positive. Exam tip: To count positive terms, use \(a_n>0\) and take the greatest integer value satisfying the inequality.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
This is an arithmetic progression with first term \(a=75\) and common difference \(d=-7\). Its \(n\)th term is \(a_n=75-7(n-1)\). For a term to be positive, \(75-7(n-1)>0\), which gives \(n<\frac{82}{7}\approx11.71\). Hence, the greatest integral value of \(n\) is 11, so 11 terms are positive. The 12th term is \(75-7\times11=-2\), so 12 terms cannot be positive. Exam tip: To count positive terms, use \(a_n>0\) and take the greatest integer value satisfying the inequality.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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