Find the missing number(?) in the following series. 1, 1.5, 2.5, 4, ? ,8.5 , 11.5

Options

A. 6
B. 5
C. 4.5
D. `5.5`

Answer

To find the missing number in the series: 1, 1.5, 2.5, 4, ?, 8.5, 11.5, we can analyze the differences between the consecutive numbers.

**Step 1: Identify the differences between consecutive terms.**

- From 1 to 1.5:
\[ 1.5 - 1 = 0.5 \]

- From 1.5 to 2.5:
\[ 2.5 - 1.5 = 1 \]

- From 2.5 to 4:
\[ 4 - 2.5 = 1.5 \]

- Now we need to find the difference from 4 to the missing number (let's call it x):

- From x to 8.5:
\[ 8.5 - x \]

- From 8.5 to 11.5:
\[ 11.5 - 8.5 = 3 \]

**Step 2: Identify the pattern in the differences.**

The differences we have calculated are:
- 0.5
- 1
- 1.5
- (x - 4)
- 3

We can see that the differences are increasing by 0.5 each time:
- 0.5, 1, 1.5, and then we can expect the next difference to be 2.

**Step 3: Calculate the missing number using the identified pattern.**

If we add 2 to the last known number (4):
\[ x = 4 + 2 = 6 \]

**Step 4: Verify the next difference.**

Now, let's check the difference from 6 to 8.5:
\[ 8.5 - 6 = 2.5 \]

Now, we can check the difference from 6 to 8.5:
- The difference from 6 to 8.5 is indeed 2.5, which follows the pattern of increasing by 0.5.

**Final Result:**

The missing number is:
\[ \boxed{6} \]

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