Final answer:
To find the next terms in the sequence 6, 8, 14, 22, 36, 58, we observe the pattern in the differences between terms, which is the sum of the previous two differences.
Using this pattern, we calculate that the next two terms in the sequence are 94 and 152.
Step-by-step explanation:
The series 6, 8, 14, 22, 36, 58 appears to be an arithmetic sequence where each term is determined by adding a specific pattern of numbers to the previous term.
To find the pattern, we can look at the differences between successive terms:
- 8 - 6 = 2
- 14 - 8 = 6
- 22 - 14 = 8
- 36 - 22 = 14
- 58 - 36 = 22
We now examine these differences to determine a secondary pattern. Upon inspection, we see that the numbers themselves are increasing in a specific manner: each new difference is the sum of the previous two differences. This gives us:
- 2 + 6 = 8
- 6 + 8 = 14
- 8 + 14 = 22
To find the next two terms in the series, we would add the last two differences (14 and 22), to get the next difference and then add it to the last term:
- Next difference: 14 + 22 = 36
- Next term in the series: 58 + 36 = 94
If we repeat this process again for the following term:
- Next difference: 22 + 36 = 58
- Next term in the series: 94 + 58 = 152
Therefore, the two terms that follow 58 in the sequence are 94 and 152.