7,17,35,63,103,? a)109 b)157 c)186 d)212 e)172
Hello,
To find the next number in the sequence 7, 17, 35, 63, 103, ? let's identify the pattern.
First, we calculate the differences between consecutive terms:
17 - 7 = 10
35 - 17 = 18
63 - 35 = 28
103 - 63 = 40
Next, we calculate the differences between these differences:
18 - 10 = 8
28 - 18 = 10
40 - 28 = 12
The second-order differences are increasing by 2 each time (8, 10, 12). If this pattern continues, the next second-order difference should be (12 + 2 = 14).
So, the next first-order difference should be:
40 + 14 = 54.
Adding this to the last term in the sequence:
103 + 54 = 157.
Therefore, the next number in the sequence is 157.
Hope it helps!