What is the (10)th term of the sequence (7,14,28,56,\ldots)?
Answer and explanation
Correct answer: 3584
This is a geometric sequence because each term is obtained by multiplying the previous term by 2. Here, the first term is \(a=7\) and the common ratio is \(r=2\). Therefore, \(a_n=ar^{n-1}\). So, \(a_{10}=7\times2^9=7\times512=3584\). The option 1792 uses \(2^8\), which gives the 9th term. Exam tip: In a geometric sequence, the exponent for the \(n\)th term is always \(n-1\).
Frequently asked questions
What is the correct answer to this question?
3584
Why is this the correct answer?
This is a geometric sequence because each term is obtained by multiplying the previous term by 2. Here, the first term is \(a=7\) and the common ratio is \(r=2\). Therefore, \(a_n=ar^{n-1}\). So, \(a_{10}=7\times2^9=7\times512=3584\). The option 1792 uses \(2^8\), which gives the 9th term. Exam tip: In a geometric sequence, the exponent for 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: nth term.
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