Question

Identify next three numbers in this sequence: 2, 8, 4, 16, 12

Answer 1

The next three numbers are 48, 44, 176

Answer 2

Answer:

2, 8, 4, 16, 12, 30, 26, 50

Step-by-step explanation:

The first is determinate the different ($d$) between each consecutive value ($a_n - a_{n-1}$).

$8 - 2 = 6\\4 - 8 = -4\\16 - 4 = 12\\12 - 16 = -4$

How you can see when the position of the number in the sequence is odd you have to sum a number $6x$ and when the position of the number in the sequence is a even number you have to substract -4.

Why $6x$? If you see the first two odd position numbers in the sequence are multiples of 6, then we made the deduction that each time that you sum a number this is a multiply of 6 and -4 is constant for each position even number.

Then for each odd position number in the sequence it's representation is of the form:

$a_{n-1} + 6x = a_n$

Where $a_{n-1}$ is the number of before, $x$ the odd position of the number in the sequence and $a_n$ is the current value of $a_n$

So the rest of the sequence is of the next form:

$12 + 6(3) = 30$

$30 -4 = 26$

$26 + 6(4) = 50$

So the final answer is $\{30, 26, 50\}$