Find an explicit formula for the sequence defined recursively by $$a _{1}=1$$ and $$a _{k}=2a _{k-1}-a _{k-2}$$ Then prove the formula is correct using mathematical induction

Question

anonymous · Answer

so what i've done so far is calcluate it out to a_5

mr.math · Answer

You have to define $a_0$ or $a_2$!

amistre64 · Answer

accounting for the typo; this is still the an = 3n+7 from before right?

anonymous · Answer

But im not seeing a pattern

anonymous · Answer

@amistre, no this is a different problem

amistre64 · Answer

hmm, then yeah, your missing information

anonymous · Answer

@mr.math, this is all thats given, what do you mean?

mr.math · Answer

This is not well-defined. Based on the formula you have for $a_k$, we should have at least one more point.

amistre64 · Answer

can you possibly manipulate it to solve for a2? or a0?

anonymous · Answer

ah crud

anonymous · Answer

i have the wrong info

amistre64 · Answer

given 2 states of unknowns in the recurssion, its optimal, if not neseccary, to have 2 basises

anonymous · Answer

The initial formula is $$a _{k}=2a _{k-1}+6$$

anonymous · Answer

a_1 = 1 still

mr.math · Answer

Yeah, now we can talk. Rewrite the question again and make sure you write it right!

anonymous · Answer

k ill post it here

mr.math · Answer

And find for me the first 4 terms if you might :D

mr.math · Answer

I need to go for some time and will be right back.

anonymous · Answer

There we go: http://openstudy.com/#/updates/4ee24839e4b0a50f5c5629c8

anonymous · Answer

k, cya