Hi,
I was attempting some psychometric tests and came across these 2 sequence questions that I couldn't figure out.

Sequence 1:
2 ? 4 6 4
What is the missing number?
The answer is supposed to be 2 according to the book.

Sequence 2:
9 16 178 ? 13259
What is the missing number?
The answer is supposed to be 1025.

I can't understand the patterns in the 2 sequences so if anyone could help me out, that would be great :D

Thanks.

Hi,
I was attempting some psychometric tests and came across these 2 sequence questions that I couldn't figure out.


Sequence 1:
2 ? 4 6 4
What is the missing number?
The answer is supposed to be 2 according to the book.

This is one solution that works, though it is rather abstract. These are the first 5 Euler Phi numbers of the first 5 composite numbers.

The Euler Phi function or Totient function, \phi(n), is the number of coprimes less than or equal to a given number. The first 5 composite numbers are 4,6,8,9,10
4 has 2 coprimes, 6 has 2 coprimes, 8 has 4 coprimes, 9 has 6 coprimes, and 10 has 4 coprimes.
Thus, the sequence 2,2,4,6,4
You can also find them by using \phi(6)=6\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)=2

\phi(n)=n\left(1-\frac{1}{p_{1}}\right)\left(1-\frac{1}{p_{2}}\right)\cdot\cdot\cdot\left(1-\frac{1}{p_{k}}\right)

Where the p's are the prime factors of n.