Question 101

$$4^{11}+4^{12}+4^{13}+4^{14}\ $$is divisible by_________.

Solution

Expression : $$4^{11}+4^{12}+4^{13}+4^{14}\ $$

= $$4^{11}(1+4+4^2+4^3)$$

= $$4^{11}\times(1+4+16+64)$$

= $$4^{11}\times(85)$$

$$\because$$ $$85$$ is divisible by 17, hence the above expression is also divisible by 17

=> Ans - (C)

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