Question

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

Answer 1

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

Answer 2

index

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

Answer 3

whats the star mean?

Answer 4

multiply *

Answer 5

nevermind

Answer 6

thank you

Answer 7

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?

Answer 8

might need to adjust for A1; tho, so lets check....

well, it dont match but i was close with it

Answer 9

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

Answer 10

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

Answer 11

write it without typing it.... prolly not

Answer 12

okay hold on ill use paint and up
load it

Answer 13

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

Answer 14

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

Answer 15

do you understand now?

Answer 16

\[a _{k}\]

Answer 17

yesss :)

Answer 18

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

Answer 19

thank you do you have time for another

Answer 20

sure

Answer 21

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

Answer 22

ok, do you now what induction is in maths?

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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?)

Answer 27

and we are very happy now :)

Answer 28

thank you

Answer 29

I have more sorry its confusing to me

Answer 30

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

Answer 31

no prob

Answer 32

I figured its a geometric sequence

Answer 33

yep it is

Answer 34

so how do I solve?

Answer 35

I dont understand the problem completely

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

It will never stop than

Answer 40

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

Answer 41

well until it hits the ground?

Answer 42

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

Answer 43

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

Answer 44

ohhh i seee :)