In the arithmetic progression (13,10,7,4,\ldots), which term is (-8)?
Answer and explanation
Correct answer: 8th term
Here, the first term is \(a=13\) and the common difference is \(d=10-13=-3\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(13+(n-1)(-3)=-8\), giving \(-3(n-1)=-21\). Hence \(n-1=7\) and \(n=8\). Therefore, \(-8\) is the eighth term. The ninth term would be \(-11\), so it is not correct. Exam tip: write the negative common difference carefully before applying the \(n\)th-term formula.
Frequently asked questions
What is the correct answer to this question?
8th term
Why is this the correct answer?
Here, the first term is \(a=13\) and the common difference is \(d=10-13=-3\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(13+(n-1)(-3)=-8\), giving \(-3(n-1)=-21\). Hence \(n-1=7\) and \(n=8\). Therefore, \(-8\) is the eighth term. The ninth term would be \(-11\), so it is not correct. Exam tip: write the negative common difference carefully before applying the \(n\)th-term formula.
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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