general formula for the series 1, 5, 23, 119, 719.... ?
I know the general formula can be (n+1)!-1, but I need a general formula purely in terms of n, so that I don't need to write a code in which I would have to iterate through 1 to n to find factorial.
Answers
Answer:
The next number in the series = 5039
Step-by-step explanation:
The series is given to be : 1, 5, 23, 119, 719, .....
1 is obtained by :
2! - 1 = 2 - 1
= 1
5 is obtained by :
3! - 1 = 6 - 1
= 5
23 is obtained by :
4! - 1 = 24 - 1
= 23
119 is obtained by :
5! - 1 = 120 - 1
= 119
719 is obtained by :
6! - 1 = 720 - 1
= 719
Similarly, The next number will be obtained by : 7! - 1
So, The next number in the series = 5040 - 1
= 5039
Given data:
1, 5, 23, 119, 719, ?
To find:
The next number in the series.
Solution:
The logic / general formula behind this series is:
Current number = [previous number - a] + b
Where, a starts with 3 and goes on incrementing by 1 from the start.
b starts with 2 and goes on incrementing by 1 from the start.
( 1 x 3 ) + 2 = 3 + 2 = 5
( 5 x 4 ) + 3 = 20 + 3 = 23
( 23 x 5 ) + 4 = 115 + 4 = 119
( 119 x 6 ) + 5 = 714 + 5 = 719
The next number in the series will be:
( 719 x 7 ) + 6 = 5033 + 6 = 5039
Therefore, the next number in the series is 5039
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