If (a=8), (r=3), and (S_4=320), what is the statement?
Answer and explanation
Correct answer: True, because \(S_4=320\)
For a geometric progression with \(r\ne1\), the sum of the first \(n\) terms is \(S_n=\frac{a(r^n-1)}{r-1}\). Thus, \(S_4=\frac{8(3^4-1)}{3-1}=\frac{8(81-1)}{2}=320\). Hence, the given statement is true. Values such as \(312\) or \(324\) result from an incorrect calculation. Exam tip: substitute \(n=4\) correctly in \(r^n\) before simplifying.
Frequently asked questions
What is the correct answer to this question?
True, because \(S_4=320\)
Why is this the correct answer?
For a geometric progression with \(r\ne1\), the sum of the first \(n\) terms is \(S_n=\frac{a(r^n-1)}{r-1}\). Thus, \(S_4=\frac{8(3^4-1)}{3-1}=\frac{8(81-1)}{2}=320\). Hence, the given statement is true. Values such as \(312\) or \(324\) result from an incorrect calculation. Exam tip: substitute \(n=4\) correctly in \(r^n\) before simplifying.
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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