Question

For the sequence given by a(little 1)=3 and a(little n)=2a (little n-1) -4, find the first three terms

Answer 1

@jim_thompson5910 @ajspeller

Answer 2

what do you have so far

Answer 3

Nothing, I honestly don't remember how to solve these

Answer 4

What is the first term \(\Large a_{1}\) ?

Answer 5

3?

Answer 6

yes

Answer 7

how about \(\Large a_{2}\) ?

Answer 8

Uh...

Answer 9

would it be 6??

Answer 10

If you aren't sure, then replace EVERY copy of 'n' with 2 in \[\Large a_{n} = 2a_{n-1} - 4\]

Answer 11

\[\Large a_{n} = 2a_{n-1} - 4\]
\[\Large a_{{\color{red}{n}}} = 2a_{{\color{red}{n}}-1} - 4\]
\[\Large a_{{\color{red}{2}}} = 2a_{{\color{red}{2}}-1} - 4\]
\[\Large a_{2} = 2a_{1} - 4\]

Answer 12

But how do you solve from that?

Answer 13

well before you said a1 = 3, which is true

so,

\[\Large a_{2} = 2a_{1} - 4\]
\[\Large a_{2} = 2(3) - 4\]
\[\Large a_{2} = ??\]

Answer 14

2?

Answer 15

yes

Answer 16

for a3, we do the same but now replace n with 3
\[\Large a_{n} = 2a_{n-1} - 4\]
\[\Large a_{{\color{red}{n}}} = 2a_{{\color{red}{n}}-1} - 4\]
\[\Large a_{{\color{red}{3}}} = 2a_{{\color{red}{3}}-1} - 4\]
\[\Large a_{3} = 2a_{2} - 4\]

Answer 17

in general, the idea is this

(nth term) = 2*(previous term just before nth term) - 4

Answer 18

so if you want the 10th term, you need to find the terms a1 through a9 since a10 relies on a9

Answer 19

so to find 3 i put in 2 for a(little 2)??

Answer 20

to find that third term, you need to use a2, yes

Answer 21

as shown in \[\Large a_{3} = 2a_{2} - 4\]

Answer 22

so 0 right?

Answer 23

good, a3 = 0

Answer 24

a1 = 3
a2 = 2
a3 = 0

Answer 25

awesome!! thanks!

Answer 26

np