Describe the pattern in each sequence and determine the next term of the sequence. 1,3,6,10,...

Your answers?

1+ 2 = 3

3 +3 = 6

6 + 4 = 10

Do the next the same way,

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.