Question : $4^{11}+4^{12}+4^{13}+4^{14}$ is divisible by:
Option 1: 7
Option 2: 14
Option 3: 17
Option 4: 9
Answer (1)
10th Jan, 2024
Correct Answer: 17
Solution :
Given:
$4^{11}+4^{12}+4^{13}+4^{14}$
= $4^{11}(1+4+4^2+4^3)$
= $4^{11}(85)$
Since 85 is divisible by 17,
Therefore, the above expression is also divisible by 17.
Hence, the correct answer is 17.
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