This problem asks us to identify the missing number in a given numerical sequence. We need to find the pattern governing the series and use it to calculate the value that should replace the question mark.

Number Series Pattern Analysis

The given number series is:

170, 197, 226, 257, ?

To find the pattern, let's calculate the difference between consecutive terms:

• Difference between the second and first term: $197 - 170 = 27$
• Difference between the third and second term: $226 - 197 = 29$
• Difference between the fourth and third term: $257 - 226 = 31$

Identifying the Underlying Pattern

Let's look at the sequence of differences we found: 27, 29, 31.

We can observe a clear pattern here: each difference is 2 more than the previous difference.

• $29 = 27 + 2$
• $31 = 29 + 2$

This indicates that the differences are increasing by 2 each time. This is sometimes called a second-order difference pattern where the differences themselves form an arithmetic progression.

Calculating the Missing Number

Following the pattern, the next difference in the sequence should be 2 more than the last calculated difference (31).

• Next difference = $31 + 2 = 33$

Now, to find the missing number (the fifth term in the series), we add this next difference (33) to the last known term in the series (257).

• Missing Number = $257 + 33$
• Missing Number = $290$

Therefore, the number that will come at the place of the question mark is 290.