Question

arithmetic sequence q :
Determine a recursive denition for each of the following sequence

see equation...

an=2n−3 (n=0,1,2...)

Answer 1

\[a_1=-1\]
\[a_2=1\]
\[a_3=3\]
\[a_4=5\]...

Answer 2

sure looks like
\[a_n=a_{n-1}+2\]

Answer 3

that doesnt work for n=1

Answer 4

?

Answer 5

this thing is just a line with slope 2. so of course you add 2 every time you go over 1.

Answer 6

btw it does work for n = 1 yes?
\[a_1=a_0+2\]

Answer 7

is there a general way of working this out (for any sequence)

i thought \[a_{0} = 0 so 0+2 ] is not -1

Answer 8

i thought :
\[a _{1} = 0 +2\]

which isn't = -1

Answer 9

Not sure how to write it like you guys but it looks like 2x-3

Answer 10

\[a_n=2n-3\]
Is that your formula?

Answer 11

yeah

Answer 12

so
\[a_0=2\times 0-3=-3\]

Answer 13

So, for instance you want 2nd term then you would plug in 2 for n
2(2)-3
4-3=1

Answer 14

it is pretty clear that
\[2n-3\] is a line with slope 2 yes? means every time n increases by 1,
\[a_n\] increases by 2

Answer 15

and y intercept of that line is at -3

Answer 16

\[a_0=2\times 0-3=-3\]
\[a_1=2\times 1-3=2-3=-1\]
\[a_2=2\times 2-3=4-3=1\]
\[a_3=2\times 3-3=6-3=3\] etc

Answer 17

so as a recursion you could say
\[a_0=-3\]
\[a_n=a_{n-1}+2\]