Given #a_1=4#, what is the 7th term of the recursive sequence using #a_n= 2a_(n-1) - 3#, for #n>=2#?
1 Answer
Explanation:
Let's look at the first few numbers in this sequence:
Now, let's look at the difference between them at each step
That sequence of numbers (1,2,4,8,...) is the sequence of the powers of two (
Now, that is fine and dandy, and will give you the answer for any number in the sequence but I (and math teachers in general) like elegant answers and I think we can come up with a better equation for the sequence.
Let's look at the sequence of powers of two next to the this sequence member by member:
Notice something interesting? Each number in our sequence is the correspondent power of two plus 3. Now we can write that:
So