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Algebra Level pending

Consider a sequence $X$ formed by adding the corresponding terms of the sequence of Prime numbers and Fibonacci numbers.

What is the difference between the $nth$ and $(n-1)th$ terms of the sequence $X$ ,where $n$ is the that term of the concernced sequence which is formed by adding a prime $x$ to the corresponding Fibonacci number.

$x$ is that prime number which is the first of it's kind to have a property of giving a composite number on reversing its digits.

The answer is 10.

1 solution

Daman Deep Singh
Apr 11, 2016

$Prime number sequence : 2, 3, 5, 7, 11, 13, 17,19,..........$ ; and $Fibonacci number sequence : 1, 1, 2, 3, 5, 8, 13, 21,.......$ ;and $sequence X : 3, 4, 7, 10, 16, 21, 30, 40,.............$ .

Now we have to find $x$ to proceed , as per the given condition $x$ is $19$ which is the $8th$ term in the prime number sequence.

Therefore, $n=8 and (n-1)=7$ ,these respective terms in the sequence $X$ are $40 and 30$ .

Hence, the required difference is $40-30=\boxed{10}$ .

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The answer is 10.

1 solution

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