AP EAMCET · Maths · Basic of Mathematics
For all integers \(n \geq 1\), which of the following is divisible by 9 ?
- A \(8^n+1\)
- B \(4^n-3 n-1\)
- C \(3^{2 n}+3 n+1\)
- D \(10^n+1\)
Answer & Solution
Correct Answer
(B) \(4^n-3 n-1\)
Step-by-step Solution
Detailed explanation
\(\because \quad 4^n=(1+3)^n\) \(=1+3 n+\frac{n(n-1)}{2 !} 3^2+\ldots\) \(\Rightarrow \quad 4^n-3 n-1=3^2\left[\frac{n(n-1)}{2 !}+\ldots\right]\) It is clear from above that \(4^n-3 n-1\) is divisible by 9 .
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