Directions: Find the missing number in the series.

38, ?, 72, 98, 130, 168

The correct answer is 52.

To find the missing number in the series, let us examine the pattern formed by the differences between consecutive terms.

Given series: 38, ?, 72, 98, 130, 168

First, let us calculate the difference between each pair of known consecutive terms from right to left:

$168-130=38$

$130-98=32$

$98-72=26$

Observing the pattern of these differences (38, 32, 26), we can see that each successive difference decreases by 6 as we move left:

$38-6=32$

$32-6=26$

Continuing this pattern to find the missing differences:

The difference before 26 should be:

$26-6=20$

The difference before 20 should be:

$20-6=14$

Now, we can find the missing number by subtracting 20 from 72:

$72-20=52$

We can also verify this by adding 14 to the first term (38):

$38+14=52$

Thus, the complete series with their respective term-to-term additions is:

38 (+14) 52 (+20) 72 (+26) 98 (+32) 130 (+38) 168

Therefore, the missing number in the series is 52.