What are the next two terms in the pattern 3, 6, 5, 10,9, 18, 17, . . .?

2 Answers
Nov 28, 2015

They could be #34#, #33#

Explanation:

This sequence seems to come from an alternating iterative rule where on odd steps you double the previous number and on even steps you subtract #1# from the previous number.

The formula for a general term of the sequence may be written:

#a_n = { (2^((n+1)/2)+1, "if n is odd"), (2^(n/2+1)+2, "if n is even") :}#

To avoid the condition on #n# being odd or even, you can use #(-1)^n# to formulate it as follows:

#a_n = (2^((n+1)/2)+1) * (1-(-1)^n)/2 + (2^(n/2+1)+2) * (1+(-1)^n)/2#

Nov 6, 2017

It's actually easier than that, unless you need a formula.

Explanation:

The pattern is: double, then subtract 1, or

multiply by 2, subtract 1.

#3*2=6# and #6-1=5#

#5*2=10# and #10-1=9#

#9*2=18# and #18-1=17#

The continuation would be:

#17*2=34# and #34-1=33#

#33*2=66# and #66-1=65#

and so on.