What comes next in the series: 4,5,8,17,44,… and why??
What number comes next in the series: 4, 5, 8, 17, 44, … and why? I believe the answer is 125. I would appreciate insights into the reasoning behind this conclusion, particularly that "why" aspect of the question.
8 Answers
s(n+1) = s(n) + 3^(n-1)
so
s(n+1) =s(1) +3^0 +3^1 +….+3^(n-1)
=4 + (3^n -1)/2
so s(n+1) =4 +(3^n-1)/2
I think I’ve got it! There’s no obvious pattern to the series, but look at the amount you’re adding each time.
5-4 = . . . 1
8-5 = . . . 3
17-8 = . . 9
44-17 = .27
The amount you add to the last number to get the next one is increasing by powers of 3. So for the next step in the series, you’d add 27*3, or 81, to 44 to get 125.
You keep multiplying by multiples of 3:
4 to 5 is 1, 5 to 8 is 3, 8 to 17 is 9, 17 to 44 is 27, 44 to 125 is 81, multiply the previous difference by 3
Feb 09, 2025
4 – 5 = 1
5 – 8 = 3 (1*3)
8 – 17 = 9 (3*3)
17 – 44 = 27 (9*3)
44 – 125 = 81 (27*3)
So, you are multipling the “distance” of the previous two numbers by three to get the new “distance”. you then add that to previous number to get the new number.
Hope that provides a bit more clarity.
Jan 31, 2025
After x comes 3x-7:
5 = 3*4-7
8 = 3*5 -7
17=3*8-7
44=3*17-7
next element is 125=3*44-7
Feb 09, 2025
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RE:
What comes next in the series: 4,5,8,17,44,… and why??
The answer is 125…emphasis on the "why" part of the question.
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