The seventh term of the sequence 1,3,6,10 ........ Is

Options

A. 20
B. 26
C. 28
D. 32

Answer

To find the seventh term of the sequence 1, 3, 6, 10, we can follow these steps:

### Step 1: Identify the sequence
The given sequence is:
1, 3, 6, 10.

### Step 2: Calculate the differences between consecutive terms
- The difference between the 1st term (1) and the 2nd term (3) is:
\(3 - 1 = 2\)

- The difference between the 2nd term (3) and the 3rd term (6) is:
\(6 - 3 = 3\)

- The difference between the 3rd term (6) and the 4th term (10) is:
\(10 - 6 = 4\)

So, the differences are:
2, 3, 4.

### Step 3: Identify the pattern in the differences
The differences are increasing by 1 each time:
- From 2 to 3, the increase is 1.
- From 3 to 4, the increase is also 1.

### Step 4: Calculate the next differences
Continuing this pattern, the next difference after 4 will be:
- 4 + 1 = 5 (for the 5th term)
- 5 + 1 = 6 (for the 6th term)
- 6 + 1 = 7 (for the 7th term)

### Step 5: Calculate the 5th term
To find the 5th term:
- 4th term (10) + 5 (next difference) = 10 + 5 = 15.

### Step 6: Calculate the 6th term
To find the 6th term:
- 5th term (15) + 6 (next difference) = 15 + 6 = 21.

### Step 7: Calculate the 7th term
To find the 7th term:
- 6th term (21) + 7 (next difference) = 21 + 7 = 28.

### Conclusion
The 7th term of the sequence is 28.

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