00:01
We want to know what is the 11th term of the sequence 15, 3, 3 fifths, 3 over 15 and so on.
00:15
So we start by looking at the last two given terms, 3 and the third and fourth term of the sequence.
00:24
We see we have 3 divided by a power of 5.
00:28
For example 3 divided by 25 is the same as 3 divided by 5 squared.
00:41
Now let's see that the previous term 3 divided by 5 is 3 divided by 5 to the power 1.
00:50
5 to the 1 is 5.
00:53
So for the fourth term the power of 5 in the denominator is 2.
01:00
For the power 5 the power of 5 in the denominator is 1.
01:06
Let's see what happens with the second term here.
01:09
If we look at the sequence this is 5 squared, this is 5 to the 1 that should be here 5 to the 0 in the denominator.
01:18
That's correct because 5 to the 0 is 1 and the result is 3 which is the second term...