not sure how to word my answer for this 5th grade problem

[mariposa1974]

What is the rule for pattern
2,4,7,14,17,34,37,74,77,154

 

[tkhunny]

Gaaaa!!! Not another one. I really wish this busy work would be extinguished. It just won't go away.

Try looking at every other number in two separate lists.

Note: There are INFINITELY many answers to this question. If you find one that you can explain, do not even consider allowing it to be marked wrong. Seriously!

 

[mmm4444bot]

I think Ted should automate sequence related problems such that they are all automatically PM'd to you

Or, to the answer mill where Soroban does most of "his" work.

 

[soroban]

Hello, mariposa1974!

What is the rule for this pattern? .\(\displaystyle 4,7,14,17,34,37,74,77,154 \)

It's rather obvious, isn't it?

\(\displaystyle \begin{array}{cccccccccccccc}4 && 7 && 14 && 17 && 34 && \hdots \\ & +\:3 && \times\:2 && +\:3 && \times\:2 && \hdots \end{array}\)

 

[tkhunny]

No, "IT" isn't. One possible solution can be broken down in this way.

 

[lookagain]

What is the rule for pattern
2,4,7,14,17,34,37,74,77,154

Yes, there are an infinite number of answers.

For other sequence problems, they could eliminate all ambiguities
by stating

"What are the next numbers (or what are the missing
numbers "inside" the sequence) if it is arithmetic, geometric,
harmonic, or something else?"

-------------------------------------------------------------

2, 2 + 5, 2 + 5 + 10, 2 + 5 + 10 + 20, 2 + 5 + 10 + 20 + 40,...

2 + 5(0) , 2 + 5(1), 2 + 5(3), 2 + 5(7), 2 + 5(15),...


0, 1, 3, 7, 15, ...

5[2^(n - 1) - 1]



2 + 5[2^((n - 1)/2) - 1]


\(\displaystyle 2 + 5(2^\frac{n - 1}{2}} - 1) , \ for \ n \ odd\)


--------------------------------------------------------------------


4, 14, 34, 74,..


4 + 0(10), 4 + 1(10), 4 + 3(10), 4 + 7(10),...


4 + 10[2^(n/2) - 1]


\(\displaystyle 4 + 10(2^{\frac{n}{2}} - 1), \ for \ n \ even\)

--------------------------------------------------------------------
--------------------------------------------------------------------


One of the possible ways:



\(\displaystyle f(n) \ = \ 2 \ + \ 5(2^{\frac{n - 1}{2}} - 1), \ for \ n \ odd\)


\(\displaystyle f(n) \ = \ 4 \ + \ 10(2^{\frac{n}{2}} - 1), \ for \ n \ even\)