Question

List the first six terms of the following sequences.
a) t1=1, tn= 1/1+tn-1 (n is greater to and equal to 2)
b) t1= 1, t2=2, tn=tn-1 - tn-2 (n is greater to and equal to 3)

Answer 1

\[\large t_1 = 1\]
\[\large t_n = \dfrac{1}{1+t_{n-1}}\]

plugin \(n=2\)

Answer 2

1/2?

Answer 3

Yes!

\[\large t_1 = 1\]
\[\large t_2 = \dfrac{1}{2}\]

\[\large t_n = \dfrac{1}{1+t_{n-1}}\]

plugin \(n=3\)

Answer 4

2/3?

Answer 5

Yep! keep going..

Answer 6

oh i see! i think i got it. 3/5, 5/8, 8/13
How do you do b)?

Answer 7

b isn't any different :
\[t_1 = 1\]
\[t_2 = 2\]
\[t_n = t_{n-1}-t_{n-2}\]

plugin \(n=3\)

Answer 8

1, then I got -1 for n=4

Answer 9

looks good

Answer 10

but the answer key says 2

Answer 11

the pattern is 1,2,1, -1,-2,-1

Answer 12

that loooks good !

Answer 13

where did we get the 2?

Answer 14

1, `2`,1, -1,-2,-1

you're talking about that `2` ?

Answer 15

yes

Answer 16

we didn't get that `2`, it was given to us
we're given first TWO terms in the question itself..

Answer 17

Notice this sequence requires you to take the difference of previous TWO terms
so you need TWO starting values as seed for the recursive sequence..

Answer 18

but for n=5, i got 0, not -2

Answer 19

look at first four terms : \[ 1,~ 2, ~1, ~ -1, \]

Answer 20

you can get the next term by taking difference of -1 and 1, yes ?
whats the value of \(-1-1\) ?

Answer 21

-2, opps forgot the neg. sign. thank you!