There is no one right answer to this type of questions. The next element can be anything you want.
That is one of the typical IQ questions of the type what is the next in a sequence, by inferring it from the previous values.
The answer is, the next item can be anything you want, the book can come up with some rules to justify the next element, but so can anyone.
For example given the sequence 1,2,3,4,5,6,7,8,9, what is the next element?
It is very easy to construct a function where the next elements will be $\pi , -1 , 0$ , ( look up Lagrange Interpolation).
This is not a logic question, the book is using a wrong example regarding (mathematical) logic.
But a constructive sequence rule like $2k, k=1,2,3,4,..,n$, will let you know how to construct the elements.
The ratio between Fibonacci numbers soon settles down to a number close to $1.618$. This number is called the Golden Ratio.
You get an extra digit every time the Fibonacci numbers have increased by a factor 10.
$1.618^4=6.854$ and $1.618^5=11.09$
Once the ratio settles down, you get at least one extra digit every five numbers. Sometimes the extra digit arrives sooner, and you only get four numbers with so many digits.
Best Answer
The third number in each sequence is the sum of the squares of the previous 2. $$2^2+6^2=4+36=40$$ $$3^2+7^2=9+49=58$$ $$6^2+5^2=36+25=61$$
Using this rule, we can do it for the missing number: $$2^2+3^2=4+9=13$$
So the correct answer is (A) 13