MathDB
Problems
Contests
National and Regional Contests
Saudi Arabia Contests
Saudi Arabia Pre-TST + Training Tests
2013 Saudi Arabia Pre-TST
4.1
4.1
Part of
2013 Saudi Arabia Pre-TST
Problems
(1)
a_{n+1} =\sqrt{a_n^2 + 1}, a_{2n_0} = 3a_{n_0}, a_{46} wanted
Source: 2013 Saudi Arabia Pre-TST 4.1
9/13/2020
Let
a
1
,
a
2
,
a
3
,
.
.
.
a_1,a_2, a_3,...
a
1
,
a
2
,
a
3
,
...
be a sequence of real numbers which satisfy the relation
a
n
+
1
=
a
n
2
+
1
a_{n+1} =\sqrt{a_n^2 + 1}
a
n
+
1
=
a
n
2
+
1
Suppose that there exists a positive integer
n
0
n_0
n
0
such that
a
2
n
0
=
3
a
n
0
a_{2n_0} = 3a_{n_0}
a
2
n
0
=
3
a
n
0
. Find the value of
a
46
a_{46}
a
46
.
Sequence
algebra
recurrence relation