In the arithmetic progression (30,27,24,21,\ldots), which term is zero?
Answer and explanation
Correct answer: 11th term
Here, the first term is \(a=30\) and the common difference is \(d=-3\). The \(n\)th term is \(a_n=a+(n-1)d\). For the term to be zero, \(30+(n-1)(-3)=0\). This gives \(30-3n+3=0\), so \(n=11\). Hence, the eleventh term is zero. The tenth term is \(3\), not zero. Exam tip: To find a term number in an AP, substitute the given term value in \(a_n\) and solve for \(n\).
Frequently asked questions
What is the correct answer to this question?
11th term
Why is this the correct answer?
Here, the first term is \(a=30\) and the common difference is \(d=-3\). The \(n\)th term is \(a_n=a+(n-1)d\). For the term to be zero, \(30+(n-1)(-3)=0\). This gives \(30-3n+3=0\), so \(n=11\). Hence, the eleventh term is zero. The tenth term is \(3\), not zero. Exam tip: To find a term number in an AP, substitute the given term value in \(a_n\) and solve for \(n\).
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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