3 100 297 594 991 (?)

Options

A. 1489
B. 1479
C. 1478
D. 1488

Explanation

To solve the series: 3, 100, 297, 594, 991, (?), we need to identify the pattern in the differences between consecutive numbers.

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

- The difference between 3 and 100:
\[ 100 - 3 = 97 \]

- The difference between 100 and 297:
\[ 297 - 100 = 197 \]

- The difference between 297 and 594:
\[ 594 - 297 = 297 \]

- The difference between 594 and 991:
\[ 991 - 594 = 397 \]

Now we have the differences:
- 97
- 197
- 297
- 397

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

The differences themselves form a series:
- 97
- 197
- 297
- 397

We can see that each difference increases by 100:
- \(197 - 97 = 100\)
- \(297 - 197 = 100\)
- \(397 - 297 = 100\)

**Step 3: Predict the next difference.**

Following the established pattern, the next difference should be:
\[ 397 + 100 = 497 \]

**Step 4: Calculate the missing number.**

Now, we add this difference to the last known term in the series (991):
\[ 991 + 497 = 1488 \]

Thus, the missing number in the series is **1488**.

**Final Answer:**
The missing number is **1488**.

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