complete the series
8, 24, 48, 80, 120, ….

Options

A. 158
B. 162
C. 164
D. 168

Explanation

To complete the series 8, 24, 48, 80, 120, we will analyze the differences between the consecutive terms and identify a pattern.

### Step 1: Identify the differences between consecutive terms
- The first term is 8.
- The second term is 24.
- The difference between the second and first term:
\( 24 - 8 = 16 \)

- The third term is 48.
- The difference between the third and second term:
\( 48 - 24 = 24 \)

- The fourth term is 80.
- The difference between the fourth and third term:
\( 80 - 48 = 32 \)

- The fifth term is 120.
- The difference between the fifth and fourth term:
\( 120 - 80 = 40 \)

So, the differences we have are:
- \( 16, 24, 32, 40 \)

### Step 2: Identify the pattern in the differences
Now, let's look at the differences we calculated:
- The difference between the first difference (16) and the second difference (24) is:
\( 24 - 16 = 8 \)

- The difference between the second difference (24) and the third difference (32) is:
\( 32 - 24 = 8 \)

- The difference between the third difference (32) and the fourth difference (40) is:
\( 40 - 32 = 8 \)

We can see that the differences between the differences are constant and equal to 8.

### Step 3: Calculate the next difference
Since the pattern in the differences is consistent, we can find the next difference by adding 8 to the last difference (40):
- Next difference = \( 40 + 8 = 48 \)

### Step 4: Calculate the next term in the series
Now, we add this new difference (48) to the last term in the series (120):
- Next term = \( 120 + 48 = 168 \)

Thus, the next number in the series is **168**.

### Final Answer:
The completed series is: 8, 24, 48, 80, 120, **168**.

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