### There is a sequence of numbers a_{1}, a_{2}, ... where a_{1} = 2, a_{2} = 3, and a_{n} =

for n ≥ 3. What is the value of a

_{756} ?

- Home
- Math
- All Questions

**Answer: **

**Step by Step Explanation: **- A series of number is given. Where a
_{1} = 2 a_{2} = 3 and a_{n} = for n ≥ 3. - On relating the sequence, a
_{1} = 2

a_{2} = 3

a_{3} = =

a_{4} = =

a_{5} = =

a_{6} = =

a_{7} = = 2

a_{8} = = 3

and so on.... - Therefore, we will get a sequence which repeat after every sixth term,

i.e. a_{1} = 2, a_{2} = 3, a_{3} = , a_{4} = , a_{5} = , a_{6} = , a_{7} = 2, a_{8} = 3 .... - As we have to find out a
_{756}. On dividing 756 by 6 which leaves a remainder of 0. So this term is equivalent to 6^{th} term i.e. a_{6}. - Thus, a
_{756} = a_{6} = .