Question

Find the pattern
1,5,17,63,161,_,_
Full explation​

Answer 1

Step-by-step explanation:

What number comes next in the series 1, 5, 17, 53, and 161?

Digits ••> 1 ••••• 5 ••••• 17 ••••• 53 ••••• 161 ••XX

Gap ••> ••| •• 4 ••|•• 12 ••|•••36•••|••108•••|•• ??••|•

Then we see that the Gap is:

4 = 1 + 3 which is ( 3 ^0 + 3^1 )

12 = 3 + 9 which is ( 3^1 + 3^2 )

36 = 9 + 27 which is ( 3^2 + 3^3 )

108 = 27 + 81 which is ( 3^3 + 3^4 )

It would therefore be logical that ne next few Gap entries were:

( 3^4 + 3^5) = ( 81 + 243 ) = ( 324 )

( 3^5 + 3^6 ) = ( 243 + 729 ) = ( 972 )

( 3^6 + 3^7 ) = ( 729 + 2187 ) = ( 2916 )

(up to)

( 3^n + 3^(n+1) ) where in this case, “ n ” is any Integer greater than 6.

The sequence (not the Gap) is therefore:

1, 5, 17, 53, 161, 324, 972, 2916 and so on.