Question

write a recursive formula for this sequence:
1,4,10,22

Answer 1

I was thinking.... this sorta works \(\large \begin{array}{ccccc}
1&2&3&4&5 \\
\hline\\
1&4&10&22&\square \\
\hline\\
&2(2-1)+2&2(3-1)+2&2(4-1)+2&2(n-1)+2\\
\end{array}\)

Answer 2

hmm.. that ... one sec

Answer 3

so that would be my recrusive formula?

Answer 4

\( \begin{array}{ccccc}
1&2&3&4&5 \\
\hline\\
1&4&10&22&\square \\
\hline\\
&2(2^{th}-1)+2&2(3^{th}-1)+2&2(4^{th}-1)+2&2(n^{th}-1)+2
\end{array}\)

Answer 5

what would be my explicit formula?

Answer 6

is more like a arithmetic series

Answer 7

well, is 2 times current term value minus 1 plus 2

so say.. if you're in the 2nd term
2nd term - 1, gives the 1st term, and thus its value

1st term value is 1
2nd will be 2 ( 1-1) +2 = 2
3rd will be 2 ( 2-1) + 2 = 4
4th will be 2( 4-1) + 2 = .....

Answer 8

hmm.... well one sec

Answer 9

well, is 2 times current term value minus 1 plus 2

so say.. if you're in the 2nd term
2nd term - 1, gives the 1st term, and thus its value

1st term value is 1
2nd term will be 2(2nd - 1)+2 = 2 ( 1)+2 = 4
3rd term will be 2(3rd - 1) + 2 = 2( 4) + 2 = 10
4th term will be 2(4th -1)+2 = 2(10)+2 = 22

Answer 10

(n-1) meaning..... the current "n term" -1
so that'd give the previous term
times 2
+2

Answer 11

no it's actually set up like this
0,1
1,4
2,10
3,22

Answer 12

its not 1,1

Answer 13

well, it'd still apply \(\large \begin{array}{ccccc}
0&1&2&3&4 \\
\hline\\
1&4&10&22&\square \\
\hline\\
&2(1^{st}-1)+2&2(2^{nd}-1)+2&2(3^{rd}-1)+2&2(n^{th}-1)+2
\end{array}\)

Answer 14

the 1st term will then be
2( 1st -1) 2(1) + 2 = 4

Answer 15

1-1=0

Answer 16

the (1-1) term, that is, the 0 term value is 1

Answer 17

okay so what's the recursive formula? im a little confused

Answer 18

the "n" stands for the CURRENT term
then you subtract 1 from it, gives you the PREVIOUS term
so (1-1) should give you the \(\bf 0^{th}\) term and thus its value, of 1

Answer 19

2(2nd - 1) will give you the 2 ( 2-1) or the 1st term, 2(1st term) whose value is 4
2(4)+2 = 10

Answer 20

so the formula is 2(nth-1)+2?

Answer 21

skipping the 1st term, I'd say yes, that'd the SERIE

Answer 22

but I can't skip the first term because it's apart of the series

Answer 23

how would that work out?

Answer 24

was thinking about that..... I figure..... the 1st one is included hmm

Answer 25

hmmm I don't see the inclusion of the 1st term .... simply enough.....

Answer 26

ok thanks