In the arithmetic progression (64,56,48,40,\ldots), which term is zero?
Answer and explanation
Correct answer: 9th term
Here, the first term is \(a=64\) and the common difference is \(d=56-64=-8\). The \(n\)th term is \(a_n=a+(n-1)d\). For the zero term, \(64+(n-1)(-8)=0\), so \(n-1=8\) and hence \(n=9\). Therefore, the ninth term is zero. The eighth term is \(8\), not zero. Exam tip: To find the position of a specified term, write the \(a_n\) formula first and substitute the given value.
Frequently asked questions
What is the correct answer to this question?
9th term
Why is this the correct answer?
Here, the first term is \(a=64\) and the common difference is \(d=56-64=-8\). The \(n\)th term is \(a_n=a+(n-1)d\). For the zero term, \(64+(n-1)(-8)=0\), so \(n-1=8\) and hence \(n=9\). Therefore, the ninth term is zero. The eighth term is \(8\), not zero. Exam tip: To find the position of a specified term, write the \(a_n\) formula first and substitute the given value.
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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