Look for a pattern and find the next two numbers in the sequence and then write a general version of the nth term.
1 2 3 4 5 6 7 8 n
18 30 42 54 66 78
I can recognize the pattern as being + 12 so under 7 my answer would be 90 and under 8 my answer would be 102, but how do I figure out what the nth term would be?
To find the nth term of a sequence, you need to identify the pattern in how the numbers are increasing or decreasing. In this case, we can see that each number in the sequence is obtained by multiplying the corresponding position number by 12 and adding 6.
Let's break down the steps to find the nth term:
1. Start by writing down the sequence: 18, 30, 42, 54, 66, 78.
2. Observe that the first term (18) can be obtained by multiplying the position number (1) by 12 and adding 6: 1 * 12 + 6 = 18.
3. Next, check if the same pattern holds for the second term (30): 2 * 12 + 6 = 30. It does!
4. Repeat this pattern for the remaining terms to confirm that it holds throughout the sequence.
Now that we have identified the pattern, we can write a general formula for the nth term:
nth term = n * 12 + 6
Using this formula, we can find any term in the sequence by replacing n with the corresponding position number. For example:
- To find the 7th term, substitute n = 7 into the formula: 7 * 12 + 6 = 90.
- To find the 8th term, substitute n = 8: 8 * 12 + 6 = 102.
Therefore, the formula for the nth term of the given sequence is: nth term = n * 12 + 6.