5, 14, 27, 44, 65, ?

Options

A. 88
B. 90
C. 109
D. 130

Explanation

To solve the series 5, 14, 27, 44, 65, ?, we will follow these steps:

### Step 1: Identify the given series
The series provided is: 5, 14, 27, 44, 65.

### Step 2: Calculate the differences between consecutive terms
We will find the differences between each pair of consecutive terms in the series:

- Difference between 14 and 5:
\( 14 - 5 = 9 \)

- Difference between 27 and 14:
\( 27 - 14 = 13 \)

- Difference between 44 and 27:
\( 44 - 27 = 17 \)

- Difference between 65 and 44:
\( 65 - 44 = 21 \)

Now we have the difference series: 9, 13, 17, 21.

### Step 3: Analyze the difference series
Next, we will look at the differences in the difference series:

- Difference between 13 and 9:
\( 13 - 9 = 4 \)

- Difference between 17 and 13:
\( 17 - 13 = 4 \)

- Difference between 21 and 17:
\( 21 - 17 = 4 \)

The differences between the differences are constant and equal to 4.

### Step 4: Predict the next difference
Since the difference increases by 4 each time, we can predict the next difference:

- Next difference:
\( 21 + 4 = 25 \)

### Step 5: Calculate the next term in the original series
Now, we will add this next difference to the last term of the original series:

- Next term:
\( 65 + 25 = 90 \)

### Conclusion
Thus, the next number in the series is **90**.

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