4^11+4^12+4^13+4^14+4^15 is divisible by which of the following?
1) 11 2)31 3)341 4) all of the above
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Step-by-step explanation:
The terms are in Geometric Progression. You can directly solve it by using GP properties. But since the series is small, you can solve it directly without the applying the concepts of GP.
4^10 is common in all the terms . So this leaves us with 4^10(1 + 4 + 16 + 64 +256) = 341 * 4^10. Hence it is divisible by powers of 2 till 2^ 20 and factors of 341 i.e, 11 and 31.
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