Direction: What should come in place of question mark in the following number series?
489 510 516 528 543 555 ?

Options

A. 569
B. 570
C. 573
D. 568

Answer

To solve the number series problem, we will analyze the given numbers step by step to identify the pattern and find the missing number.

**Given Series:**
489, 510, 516, 528, 543, 555, ?

### Step 1: Identify the Differences
First, we will calculate the differences between consecutive numbers in the series.

- Difference between 510 and 489:
\( 510 - 489 = 21 \)

- Difference between 516 and 510:
\( 516 - 510 = 6 \)

- Difference between 528 and 516:
\( 528 - 516 = 12 \)

- Difference between 543 and 528:
\( 543 - 528 = 15 \)

- Difference between 555 and 543:
\( 555 - 543 = 12 \)

### Summary of Differences:
- 21, 6, 12, 15, 12

### Step 2: Analyze the Pattern
Now, we will analyze the differences to see if there is a pattern.

- The differences are:
21, 6, 12, 15, 12

It appears that the differences do not follow a simple arithmetic pattern, but we can analyze them further.

### Step 3: Calculate the Next Difference
To find the next number in the series, we need to identify the next difference.

Looking at the last few differences:
- 15 (from 528 to 543)
- 12 (from 543 to 555)

We can see that the differences are alternating. If we follow the pattern, the next difference after 12 could be 15 again.

### Step 4: Add the Next Difference
Now we will add this difference to the last number in the series:

- Last number: 555
- Next difference: 15

So, we calculate:
\( 555 + 15 = 570 \)

### Conclusion
The missing number in the series is **570**.

### Final Answer:
**570**

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