1 Question Algebra 2

Question

anonymous · Answer

attachment

usukidoll · Answer

Recursion is the process of choosing a starting term and repeatedly applying the same process to each term to arrive at the following term.  Recursion requires that you know the value of the term immediately before the term you are trying to find.

jack1 · Answer

yay, cheers @KimberlyAlice  and @UsukiDoll ;P

anonymous · Answer

Okay, so how would I find the equation for this problem?

Thanks @Jack1  :P

usukidoll · Answer

so examples of recursion formulas are 
$$a_1 = 4, a_n = 2a_{n-1}$$
or 
$$a_1=4 , a_{n+1} = 2a_n$$

usukidoll · Answer

so what is the $$a_1 $$ in this problem?

usukidoll · Answer

we need to know what a_1 is or we are stuck

anonymous · Answer

a1 would be the recursive number?

usukidoll · Answer

well we need to figure out the next term  it's like a chain.. but we need it to start at $$a_n $$ where n = 1

usukidoll · Answer

what's the starting number? that's a_n when n =1

anonymous · Answer

7

usukidoll · Answer

ok.. so $$\large a_1=7$$

anonymous · Answer

That limits the choices to B and D

usukidoll · Answer

so now we need to figure out ... we need to get to 4 somehow
but what recursion formula will allow us to do that

anonymous · Answer

B

anonymous · Answer

No wait...we would get 3

usukidoll · Answer

yeah that's what I mean.. we need to get to 4's land

usukidoll · Answer

we know the difference in each number is 3

anonymous · Answer

Yes

anonymous · Answer

So it would be B?

usukidoll · Answer

let me think...

usukidoll · Answer

alright our starting point is $$a_1 = 7 $$ so now we need a formula to get to 4

usukidoll · Answer

OH how I wish I can do this 
$$a_n=a_{n-1}-3 $$ where n = 2
$$a_2=a_{2-1}-3 $$ 
$$a_2=a_{1}-3 $$ 

since $$a_1 = 7$$
$$a_2=7-3 $$ 
$$a_2=4 $$

usukidoll · Answer

ok I think the multiple choices are flawed. Just look what I've done.. I got a_2 to appear as 4

usukidoll · Answer

hey! There's a typo in your choices. You want the last choice with a - sign instead

anonymous · Answer

oh no...

usukidoll · Answer

And I'll prove it 

so now we have $$a_1 = 7, a_2 =4$$
so now our next recursive formula
$$a_n=a_{n-1}-3 $$
let n = 3
$$a_3=a_{3-1}-3$$
$$a_3=a_{2}-3$$
since $$a_2=4 $$
$$a_3=4-3$$
$$a_3=1$$

usukidoll · Answer

see the pattern ... Now I have 7 4 1

usukidoll · Answer

so I have to do this 3 more times... for -2 -5 and ?!

anonymous · Answer

I'm confused...which answer choice is this?

usukidoll · Answer

or maybe not.. 

$$a_4 = -2, a_5 = -5$$

usukidoll · Answer

there's a typo in the choice we need

anonymous · Answer

But it would be D?

usukidoll · Answer

but.. .we can use the formula I have to get our next number.. we know that a_1 = 7 we need a_6

usukidoll · Answer

$${a_6}=a_{6-1}-3$$
$${a_6}=a_{5}-3$$
since $$a_5= -5$$
$${a_6}=-5-3$$
$${a_6}=-8$$

usukidoll · Answer

It's the last choice with that typo that shouldn't be there.!!!!

usukidoll · Answer

because should that stand... a_1 would've been 10 if it was subtraction it would've been 4

jack1 · Answer

why not $\Large a_n = 10 -3(n)$?

jack1 · Answer

@UsukiDoll doesnt that fit?

usukidoll · Answer

look at the choices we are given

jack1 · Answer

ah, my bad, sorry :/

usukidoll · Answer

it's the last choice with the typo. trust me! We got the beginning which is a_1 is 7
we needed to find a_6 which is -8

anonymous · Answer

Thank you for all your help @Jack1 and @UsukiDoll

jack1 · Answer

np but psh, was all @UsukiDoll , i did nothing

usukidoll · Answer

"because should that stand... a_1 would've been 10 if it was subtraction it would've been 4 "
oy I meant a_2 would've been 10 if we had a +
a_1 = 7
a_2 =4
a_3 =1
a_4 =-2
a_5 = -5
a_6 = -8

but the formula is
$$\large a_n=a_{n-1}-3 $$

anonymous · Answer

I understand. thank you!