### There is a sequence of numbers a1, a2, ... where a1 = 2, a2 = 3, and an =  an-1an-2   for n ≥ 3. What is the value of a756 ?

 2 3

Step by Step Explanation:
1. A series of number is given. Where a1 = 2 a2 = 3 and an =
 an-1 an-2
for n ≥ 3.
2. On relating the sequence, a1 = 2
a2 = 3
a3 =
 a2 a1
=
 3 2

a4 =
 a3 a2
=
 1 2

a5 =
 a4 a3
=
 1 3

a6 =
 a5 a4
=
 2 3

a7 =
 a6 a2
= 2
a8 =
 a7 a6
= 3
and so on....
3. Therefore, we will get a sequence which repeat after every sixth term,
i.e. a1 = 2, a2 = 3, a3 =
 3 2
, a4 =
 1 2
, a5 =
 1 3
, a6 =
 2 3
, a7 = 2, a8 = 3 ....
4. As we have to find out a756. On dividing 756 by 6 which leaves a remainder of 0. So this term is equivalent to 6th term i.e. a6.
5. Thus, a756 = a6 =
 2 3
.