Sequence Ak= 2a (k-1) - 3 if a1 =4 whats next 3 terms

- anonymous

Sequence Ak= 2a (k-1) - 3 if a1 =4 whats next 3 terms

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- anonymous

K-1 is supposed to be low like a exponent but at bottom idk what its called?

- anonymous

index
A2=2*4-3=5
A3=2*5-3=7
A4=2*7-3=11
A5=2*11-3=18
and so on

- anonymous

whats the star mean?

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## More answers

- anonymous

multiply *

- anonymous

nevermind

- anonymous

thank you

- amistre64

An = 2(An-1) -3
An = 2^2 (An-2) - 2(3) - 3
An = 2^3 (An-3) - 2^2(3) - 2(3) - 3
An = 2^n(A0) - 3[x]
x = 1 + 2 + 2^2 + 2^3 + ... + 2^n-1
2x = 2 + 2^2 + 2^3 + ... + 2^n-1 + 2^n
2x - x = 2^n - 1
x = (2^n -1)/2
An = 2^n(A0) - 3[(2^n -1)/2] perhaps?

- amistre64

might need to adjust for A1; tho, so lets check....
well, it dont match but i was close with it

- anonymous

is there a way I can write it with out typing so i can show you exactly how it looks

- amistre64

A1 = 4
A2= 2(4) - 3 = 5
A3= 2(5) - 3 = 7
A4= 2(7) - 3 = 11 is correct tho

- amistre64

write it without typing it.... prolly not

- anonymous

okay hold on ill use paint and up
load it

- anonymous

or like this maybe you'll understand
A = 2A -3
k (k-1)

- anonymous

but the k supposed to be up closer next to the a but set a little lower same for (k-1) Like when you do a LOG

- anonymous

do you understand now?

- anonymous

\[a _{k}\]

- anonymous

yesss :)

- anonymous

the solution is what I wrote, I cannot understand what amistre wrote :)

- anonymous

thank you do you have time for another

- anonymous

sure

- anonymous

Use mathematical induction 7+ 14+ 21+ 21 +28 +.....7N= 7N(N+1)/ 2

- anonymous

ok, do you now what induction is in maths?

- anonymous

7n(N+1) is all divided by 2 and not really

- anonymous

I know how to prove P(1) true but (k+1) is where im lost

- anonymous

induction is a technique to prove things
has 3 steps
1. what you wrote: prove that it is true for N=1
2. Assume that it is true for any N
3. Prove that it is true for N+1

- anonymous

1. N=1 7=7*1(1+1)/2=7 we are happy :)
2. (called inductive step) Suppose this is true: 7+ 14+ 21+ 21 +28 +.....7N= 7N(N+1)/ 2
3. prove it for N+1 (we can use the inductive step)
7+ 14+ 21+ 21 +28 +.....7N+7(N+1)=
this bit is
7+ 14+ 21+ 21 +28 +.....7N=7N(N+1)/ 2
so the whole is 7N(N+1)/ 2 +7(N+1)= 7(N+1)(N/2+1)=7(N+1)(N+2)/2
This completes the proof.
(can you see why?)

- anonymous

and we are very happy now :)

- anonymous

thank you

- anonymous

I have more sorry its confusing to me

- anonymous

A ball bounces 400 ft every second after that its (3/4) how many times does it bounce til it completely stops

- anonymous

no prob

- anonymous

I figured its a geometric sequence

- anonymous

yep it is

- anonymous

so how do I solve?

- anonymous

I dont understand the problem completely

- anonymous

after that its (3/4)
what does this mean?

- anonymous

so the common ratio is 3/4 400, 300... and so on

- anonymous

so 3/4 of 300 then the next and next.. but I need to find out how many times it bounces til it stops

- anonymous

It will never stop than

- anonymous

a number multiplied by 3/4 a lot of times will be a small number but will never reach 0
in maths we say it is tending to 0 as we tend to infinity

- anonymous

well until it hits the ground?

- anonymous

oh I am stupid, I think it asks for the use of this formula:
a/(1-r)

- anonymous

here a=400 1-r=1/4
so the result is 1600

- anonymous

ohhh i seee :)

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