Can someone help explain the recursive process for arithmetic sequences? I understand what the equation is I just have no clue how to put the sequence into the equation.

Question

turingtest · Answer

can you be more specific, like post the actual question or something?

amistre64 · Answer

given a starting value:  a0 (or a1 depending on text)

each new term is defined as the one before it, plus some constant amount

lets say the first term is 2,  and we want to add 3 to get to the next term

a0 = 2
a1 = 2 + 3
a2 = 2 +3+3
a3 = 2 +3+3+3
a4 = 2 +3+3+3+3

...
an = 2 + (3+3+3+3+...+3); n times

an = a0 + 3n

anonymous · Answer

This is part of an assignment. This is the question. Planning is crucial in the early stages of this project. Demonstrate how a recursive process will allow you to find the number of coins and points on all levels up to level 5. This is what I have so far.

amistre64 · Answer

your points are arithmetic .... 

your coins seem gemtric to me

anonymous · Answer

So I would do this?
a0=1+3
a1=1+3+3
a2=1+3+3+3
a3=1+3+3+3+3
a4=1+3+3+3+3+3
a5=1+3+3+3+3+3+3

anonymous · Answer

The coins are supposed to be geometric. This is the first question. Create the data to fill in the tables below. The Coins table must be an arithmetic sequence and the Points table must be a geometric sequence. The common difference or ratio cannot equal 1 or 0.

amistre64 · Answer

theres an error in the instructions ...

anonymous · Answer

Really? Is there a way for the reclusive process where you do the same thing just multiplied?
like 
a0=1*2
a1=1*2*2
 and so forth

amistre64 · Answer

your data is best fit for starting at a1, not a0 so we can adjust for that as

we are already at a1, then it goes to figure that we are already 3 more than a0

a1 = a0 + 3

a0 = 3 - a1 = -2

an = -2 + 3d

amistre64 · Answer

geometric, isa common ratio multiplied to get the new term

g0 = k
g1 = kr
g2 = krr
g3 = krrr
g4 = krrrr
....
gn = kr^n

and adjusted for your case since we start at g1

g1 = g0 r

g0 = g1/r

anonymous · Answer

That makes sense

amistre64 · Answer

you have an odd ball in your coins tho;  the first and second values are not geomtric with the rest of them.

amistre64 · Answer

2^1 = 2  <--- odd ball,  your chart has 1

the rest of them follow a geometric progression 

2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32

anonymous · Answer

Awesome! Thank you! @amistre64

amistre64 · Answer

good luck :)