To find the nth term of the given sequence, we first need to identify the pattern. In this case, we can observe that each term in the sequence is obtained by multiplying the position of the term by 12.
Let's break it down step by step:
1. Write down the sequence:
1, 2, 3, 4, 5, 6, 7, 8
2. Write down the corresponding terms in the second row:
18, 30, 42, 54, 66, 78
3. Identify the difference between the terms in the second row:
The differences are 12, 12, 12, 12, 12
4. Write down the differences in the third row:
12, 12, 12, 12, 12
5. Now, the third row gives us a constant difference of 12 between each term. This tells us that the sequence follows an arithmetic progression.
6. To find the next term after 8, we can simply add 12:
78 + 12 = 90
7. Similarly, to find the term after 90, we add 12 again:
90 + 12 = 102
From this pattern, we can generalize the nth term using the formula for arithmetic progressions:
nth term = a + (n - 1) * d
where:
- a is the first term in the sequence (18 in this case)
- n is the position of the term in the sequence
- d is the common difference between consecutive terms (12 in this case)
So, the general formula for the nth term in this sequence is:
nth term = 18 + (n - 1) * 12
By substituting the value of n, you can find any term in the sequence.