To find the 50th term of the sequence, we first need to identify the pattern in the given numbers: 4, 2, 8, 14.
Let’s examine the differences between consecutive terms:
- 2 – 4 = -2
- 8 – 2 = 6
- 14 – 8 = 6
We see that the first term decreases by 2, but then the differences stabilize at 6. This suggests that the sequence could possibly switch patterns.
Now, let’s find the next terms based on this observed pattern:
- After 14, if we continue adding 6: 14 + 6 = 20
- 20 + 6 = 26
- 26 + 6 = 32
From the second term onward, the sequence seems to be a linear progression where we begin at the second term (2) and add 6 sequentially. If we denote the **n-th** term of this linear sequence starting with 2 as:
a(n) = 2 + 6(n – 2)
With this formula, we can compute the 50th term. Here, **n** will be 50:
a(50) = 2 + 6(50 – 2)
a(50) = 2 + 6 * 48
a(50) = 2 + 288
a(50) = 290
Thus, the 50th term of the sequence is 290.