Find the next term of the following patterns
55, 109, 217, 433,…..

Options

A. 543
B. 632
C. 476
D. 865

Answer

To find the next term in the pattern 55, 109, 217, 433, we will analyze the differences between the consecutive terms and identify any patterns.

### Step 1: Identify the differences between the terms
- The first term is 55.
- The second term is 109.
- The third term is 217.
- The fourth term is 433.

Now, let's calculate the differences:
- Difference between 109 and 55:
\( 109 - 55 = 54 \)

- Difference between 217 and 109:
\( 217 - 109 = 108 \)

- Difference between 433 and 217:
\( 433 - 217 = 216 \)

So, the differences are:
- First difference: 54
- Second difference: 108
- Third difference: 216

### Step 2: Analyze the differences
Now we have the differences: 54, 108, and 216.

Let's observe the pattern in the differences:
- The second difference (108) is \( 54 \times 2 \).
- The third difference (216) is \( 108 \times 2 \).

This indicates that each difference is multiplied by 2 to get the next difference.

### Step 3: Calculate the next difference
Following the pattern, the next difference will be:
- Fourth difference: \( 216 \times 2 = 432 \)

### Step 4: Find the next term
Now, we add this next difference to the last term in the series:
- Last term: 433
- Next difference: 432

So, the next term will be:
\[ 433 + 432 = 865 \]

### Conclusion
The next term in the pattern is **865**.

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