Final answer:
To find the fourth term in the arithmetic progression, we first determined the common difference by solving for 'a' in the provided sequence. With 'a' equaling 2, we found that the common difference is 6. Thus, the fourth term is 20.
Step-by-step explanation:
To find the fourth term in the arithmetic sequence provided, we first need to identify the common difference (d) of the sequence. We know the first three terms are a, 2a + 4, and 6a + 2. The common difference between consecutive terms in an arithmetic progression is constant. Thus, the difference between the second and first term should equal the difference between the third and second term.
To find d, we calculate:
- (2a + 4) - a = a + 4
- (6a + 2) - (2a + 4) = 4a - 2
Since these two differences must be equal (because the sequence is arithmetic), we set them equal to each other and solve for a:
a + 4 = 4a - 2
3a - 6 = 0
a = 2
Now that we have a, we can find the common difference d by substituting a into one of the differences we calculated:
d = (2a + 4) - a = (2(2) + 4) - 2 = 6
Therefore, the common difference of the sequence is 6. The fourth term can be calculated by adding d to the third term:
Fourth term = (6a + 2) + 6 = (6(2) + 2) + 6 = 12 + 2 + 6 = 20
The fourth term of the sequence is 20.