Answer:
2, 8, 4, 16, 12, 30, 26, 50
Step-by-step explanation:
The first is determinate the different ([tex]d[/tex]) between each consecutive value ([tex]a_n - a_{n-1}[/tex]).
[tex]8 - 2 = 6\\4 - 8 = -4\\16 - 4 = 12\\12 - 16 = -4\\[/tex]
How you can see when the position of the number in the sequence is odd you have to sum a number [tex]6x[/tex] and when the position of the number in the sequence is a even number you have to substract -4.
Why [tex]6x[/tex]? 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:
[tex]a_{n-1} + 6x = a_n[/tex]
Where [tex]a_{n-1}[/tex] is the number of before, [tex]x[/tex] the odd position of the number in the sequence and [tex]a_n[/tex] is the current value of [tex]a_n[/tex]
So the rest of the sequence is of the next form:
[tex]12 + 6(3) = 30[/tex]
[tex]30 -4 = 26[/tex]
[tex]26 + 6(4) = 50[/tex]
So the final answer is [tex]\{30, 26, 50\}[/tex]
