Question

Find the first six terms of the sequence.

a1 = -3, an = 2 ● an-1

Answer 1

hi

Answer 2

what is that big dot?

Answer 3

\[\large a_1=-3,a_n=2a_{n-1}\]

Answer 4

lol idk i just copied and pasted the problem XD i think its a multiplication sign though

Answer 5

this means the first term is \(-3\) and to get to the next term you multiply by \(2\)

Answer 6

.-. so i subtract 3 from a number and then multiply what i get by 2?

Answer 7

in other words,\[a_1=-3,\\a_2=2\times (-3)=-6\\
a_3=2\times (-6)=-12\] and so on

Answer 8

no don't subtract, just keep multiplying by \(2\)

Answer 9

oh so then its -3, -6, -12, -24, -48, -96?

Answer 10

yup

Answer 11

wait would it be that or this? -6, -12, -24, -48, -96, -192

Answer 12

hope it is clear from the subscripts
\[a_n=2a_{n-1}\] means the next term is \(2\) times the previous one

Answer 13

says "first six" and the first one is \(-3\)

Answer 14

okay but how do i do it backwards such as this? Find an explicit rule for the nth term of the sequence.

2, -8, 32, -128, ...

Answer 15

looks to me like you are multiplying by \(-4\) each time

Answer 16

so you could say \[a_1=2,a_n=-4\times a_{n-1}\]

Answer 17

or use a big ugly dot instead of the \(\times\)

Answer 18

XD hey i think its a cute dot

Answer 19

\[\bullet\]
\[\odot\]

Answer 20

couldnt you also write that as 2 x (-4)^n-1

Answer 21

no

Answer 22

oh, doh, yes!

Answer 23

yay c:

Answer 24

that is the closed form
i wrote the recursion

Answer 25

.-. no idea what you just said

Answer 26

recursion is the one where you say what to do to the previous term to get the next term

Answer 27

oh that makes sense c: okay thank you c:

Answer 28

\[a_1=2,a_n=-4\times a_{n-1}\] is a recursion
the one you wrote
\[a_n=2\times (-4)^{n-1}\] is the "closed form" meaning if you just plug in \(n\)

Answer 29

yw