anonymous
  • anonymous
1 Question Algebra 2
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
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UsukiDoll
  • UsukiDoll
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
  • Jack1
yay, cheers @KimberlyAlice and @UsukiDoll ;P

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anonymous
  • anonymous
Okay, so how would I find the equation for this problem? Thanks @Jack1 :P
UsukiDoll
  • UsukiDoll
so examples of recursion formulas are \[a_1 = 4, a_n = 2a_{n-1}\] or \[a_1=4 , a_{n+1} = 2a_n\]
UsukiDoll
  • UsukiDoll
so what is the \[a_1 \] in this problem?
UsukiDoll
  • UsukiDoll
we need to know what a_1 is or we are stuck
anonymous
  • anonymous
a1 would be the recursive number?
UsukiDoll
  • UsukiDoll
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
  • UsukiDoll
what's the starting number? that's a_n when n =1
anonymous
  • anonymous
7
UsukiDoll
  • UsukiDoll
ok.. so \[\large a_1=7\]
anonymous
  • anonymous
That limits the choices to B and D
UsukiDoll
  • UsukiDoll
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
  • anonymous
B
anonymous
  • anonymous
No wait...we would get 3
UsukiDoll
  • UsukiDoll
yeah that's what I mean.. we need to get to 4's land
UsukiDoll
  • UsukiDoll
we know the difference in each number is 3
anonymous
  • anonymous
Yes
anonymous
  • anonymous
So it would be B?
UsukiDoll
  • UsukiDoll
let me think...
UsukiDoll
  • UsukiDoll
alright our starting point is \[a_1 = 7 \] so now we need a formula to get to 4
UsukiDoll
  • UsukiDoll
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
  • UsukiDoll
ok I think the multiple choices are flawed. Just look what I've done.. I got a_2 to appear as 4
UsukiDoll
  • UsukiDoll
hey! There's a typo in your choices. You want the last choice with a - sign instead
anonymous
  • anonymous
oh no...
UsukiDoll
  • UsukiDoll
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
  • UsukiDoll
see the pattern ... Now I have 7 4 1
UsukiDoll
  • UsukiDoll
so I have to do this 3 more times... for -2 -5 and ?!
anonymous
  • anonymous
I'm confused...which answer choice is this?
UsukiDoll
  • UsukiDoll
or maybe not.. \[a_4 = -2, a_5 = -5\]
UsukiDoll
  • UsukiDoll
there's a typo in the choice we need
anonymous
  • anonymous
But it would be D?
UsukiDoll
  • UsukiDoll
but.. .we can use the formula I have to get our next number.. we know that a_1 = 7 we need a_6
UsukiDoll
  • UsukiDoll
\[{a_6}=a_{6-1}-3\] \[{a_6}=a_{5}-3\] since \[a_5= -5\] \[{a_6}=-5-3\] \[{a_6}=-8\]
UsukiDoll
  • UsukiDoll
It's the last choice with that typo that shouldn't be there.!!!!
UsukiDoll
  • UsukiDoll
because should that stand... a_1 would've been 10 if it was subtraction it would've been 4
Jack1
  • Jack1
why not \(\Large a_n = 10 -3(n)\)?
Jack1
  • Jack1
@UsukiDoll doesnt that fit?
UsukiDoll
  • UsukiDoll
look at the choices we are given
Jack1
  • Jack1
ah, my bad, sorry :/
UsukiDoll
  • UsukiDoll
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
  • anonymous
Thank you for all your help @Jack1 and @UsukiDoll
Jack1
  • Jack1
np but psh, was all @UsukiDoll , i did nothing
UsukiDoll
  • UsukiDoll
"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
  • anonymous
I understand. thank you!

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