Describe the pattern in each sequence and determine the next term of the sequence. 1,3,6,10,...
4,13,22,31,...
1+ 2 = 3
3 +3 = 6
6 + 4 = 10
Do the next the same way,
Your answers?
For the first sequence, the pattern is that each term is obtained by adding the next consecutive integer.
Starting with 1, we add 2 to get 3. Then, we add 3 to get 6. Finally, we add 4 to get 10.
Therefore, the next term in the sequence would be found by adding 5 to the current term, which would give us 10 + 5 = 15.
So, the next term in the sequence is 15.
For the second sequence, the pattern is that each term is obtained by adding 9 to the previous term.
Starting with 4, we add 9 to get 13. Then, we add 9 to get 22. Finally, we add 9 to get 31.
Therefore, the next term in the sequence would be found by adding 9 to the current term, which would give us 31 + 9 = 40.
So, the next term in the sequence is 40.
To identify the pattern in each sequence and determine the next term, let's analyze each one separately:
Sequence 1: 1, 3, 6, 10,...
Looking at the sequence, we can observe that each term is the sum of consecutive positive integers. Let's break it down:
- The first term is 1.
- The second term can be found by adding 1 (the first positive integer) to the previous term: 1 + 1 = 2.
- The third term is found by adding 2 (the second positive integer) to the previous term: 2 + 2 = 4.
- The fourth term is found by adding 3 (the third positive integer) to the previous term: 4 + 3 = 7.
Based on this analysis, we can see that the pattern is to add consecutive positive integers to the previous term. Therefore, the next term in the sequence would be 10 + 4 = 14.
So, the next term in Sequence 1 is 14.
Sequence 2: 4, 13, 22, 31,...
Examining this sequence, we can see that each term is obtained by adding 9 to the previous term. Let's break it down:
- The first term is 4.
- The second term can be found by adding 9 to the previous term: 4 + 9 = 13.
- The third term is found by adding 9 to the previous term: 13 + 9 = 22.
- The fourth term is found by adding 9 to the previous term: 22 + 9 = 31.
Based on this pattern, we can determine that the next term in the sequence would be 31 + 9 = 40.
So, the next term in Sequence 2 is 40.
To summarize:
- The next term in Sequence 1 is 14.
- The next term in Sequence 2 is 40.