Number Series Logic: Finding the Missing Term

The question asks to find the missing number in the sequence: 20, 35, 60, 105, 190, ____.

We need to identify the pattern governing this series.

Analyzing the Series Pattern

Let's examine the differences between consecutive terms:

• $35 - 20 = 15$
• $60 - 35 = 25$
• $105 - 60 = 45$
• $190 - 105 = 85$

The sequence of differences is: 15, 25, 45, 85.

Now, let's look at the differences between these differences (second-level differences):

• $25 - 15 = 10$
• $45 - 25 = 20$
• $85 - 45 = 40$

The second-level differences are 10, 20, 40. We observe that each term is double the previous term ($10 \times 2 = 20$, $20 \times 2 = 40$).

Calculating the Next Term

Following this pattern, the next second-level difference should be $40 \times 2 = 80$.

Using this to find the next first-level difference:

• Previous difference was 85.
• Next difference = $85 + 80 = 165$.

Finally, to find the missing number in the original series, add this next difference to the last known term:

• Last term = 190.
• Missing number = $190 + 165 = 355$.

Thus, the missing number in the series is 355.