What is the pattern for 2,6,4,12,10,30,28
looks like a combination recursion
let term(n) be the nth term,
term(1) = 2
if n is odd: term(n) = 3term(n-1)
if n is even: term(n)= term(n-1) - 2
so the next terms are:
26, 78, 76, 228, 226, 678 .....
I don't know it always works
To identify the pattern in the given sequence 2, 6, 4, 12, 10, 30, 28, we need to examine the relationship between the numbers.
The pattern appears to be alternating between two separate sequences: one increasing and the other decreasing.
Let's break down the given sequence into two separate patterns:
Pattern 1: Increasing sequence
2, 4, 10, 28
Pattern 2: Decreasing sequence
6, 12, 30
Now, let's analyze each pattern separately:
Pattern 1: Increasing sequence
Starting with 2, each term in this sequence is obtained by multiplying the previous term by 2 and then subtracting 2:
2 * 2 - 2 = 4
4 * 2 - 2 = 10
10 * 2 - 2 = 28
Pattern 2: Decreasing sequence
Starting with 6, each term in this sequence is obtained by multiplying the previous term by 2 and then subtracting 6:
6 * 2 - 6 = 6
6 * 2 - 6 = 12
12 * 2 - 6 = 30
So, the pattern for the given sequence is:
2, (2 * previous term - 2), 4, (2 * previous term - 2), 10, (2 * previous term - 6), 28
Using this pattern, we can continue the sequence by applying the same formulas.