If \(a_n=16\cdot\left(\frac{1}{2}\right)^{n-1}\), what is the value of \(a_4\)?
Answer and explanation
Correct answer: 2
The governing concept is the explicit formula for the general term of a geometric progression, \(a_n=a_1r^{n-1}\). To find \(a_4\), substitute \(n=4\): \(a_4=16\left(\frac12\right)^{4-1}=16\left(\frac12\right)^3\). Since \(\left(\frac12\right)^3=\frac18\), the result is \(16\times\frac18=2\). Therefore, option B is correct. Option C would come from using only two halvings, and option 8 ignores the multiplication by the initial coefficient. The exponent must be \(n-1\), not \(n\).
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The governing concept is the explicit formula for the general term of a geometric progression, \(a_n=a_1r^{n-1}\). To find \(a_4\), substitute \(n=4\): \(a_4=16\left(\frac12\right)^{4-1}=16\left(\frac12\right)^3\). Since \(\left(\frac12\right)^3=\frac18\), the result is \(16\times\frac18=2\). Therefore, option B is correct. Option C would come from using only two halvings, and option 8 ignores the multiplication by the initial coefficient. The exponent must be \(n-1\), not \(n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Geometric Progression.
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