Guess the rule and add the next number in the sequence.

7, 10, 16, 25, 37,

Step-by-step explanation:

Let us first closely examine the sequence for any mathematical correlation between the terms of sequence.

It is visualized that the series is progressing with addition of increasing even numbers starting with + 6 (+6, + 8, + 10, + 12, + 14, + 16, + 18 ...) in the previous term to obtain next terms of the series. This logic continues for entire series.

The given series is:

1,7,15,25,37

Starting with first number of the series

1

1 + 6 = 7

7 + 8 = 15

15 + 10 = 25

25 + 12 = 37

37 + 14 = 51

51 + 16 = 67

67 + 18 = 85

The extended series is

1, 7, 15, 25, 37, 51, 67, 85