Question

Find the first five terms of the given recursively defined sequence.

A[n]= 1/ 1+ A[n]-1 and A1=2

A[2]=
A[3]=
A[4]=
A[5]=

Answer 1

is this
\[a_n=\frac{1}{1+a_{n-1}}\]?

Answer 2

Yes

Answer 3

ok so first we fine
\[a_2\] via
\[a_2=\frac{1}{1+a_1}=\frac{1}{1+2}=\frac{1}{3}\]

Answer 4

Why don't we subtract 2-1= 1/2

Answer 5

then repeat the process to find
\[a_3=\frac{1}{1+a_2}=\frac{1}{1+\frac{1}{3}}=\frac{1}{\frac{4}{3}}=\frac{3}{4}\]

Answer 6

the subscript does not mean subtract the term. the subscript is like saying
"first term"
"second term"
"third term"
and so on

Answer 7

so this statement
\[a_n=\frac{1}{1+a_{n-1}}\] means the "nth" term is found by taking one over one plus the previous term

Answer 8

Oh ok...

Answer 9

so a4=7/4 and a5= 11/4

Answer 10

\[a_4=\frac{1}{1+a_3}=\frac{1}{1+\frac{3}{4}}=\frac{1}{\frac{7}{4}}=\frac{4}{7}\] right

Answer 11

but that is not what i get for the next term

Answer 12

i get
\[a_5=\frac{1}{1+a_4}=\frac{1}{1+\frac{4}{7}}=\frac{1}{\frac{11}{7}}=\frac{7}{11}\]

Answer 13

why is not what i had?

Answer 14

you had 11/4 but my arithmetic gave 7/11