00:01
We have the sequence where any term can be written as 5 n squared plus 1.
00:04
Now, is this an arithmetic sequence or a geometric sequence? let's test first for arithmetic.
00:10
An arithmetic sequence will have a common difference of d, where any term minus the previous will be equal, no matter which two terms we pick.
00:19
So let's calculate a couple of terms so we can figure out what d is.
00:22
The first term, that will have n equal to 1, so we'll have 5 times 1 plus 1, which is 6, then the second term, that will be 5 times 2 squared or 4 plus 1, which is 21.
00:37
And the third term will be 5 times 3 squared, which is 9 plus 1.
00:43
So that's 45 plus 1 or 46.
00:47
Now let's see if we can calculate d.
00:50
So we'll have 46 minus 21, and this should be equal to 21 minus 6.
00:57
But unfortunately, that's just not the case.
00:59
21 minus 6 is 15, whereas 46 minus 21 is 25.
01:08
And 25 does not equal 15...