00:01
We have a geometric progression, which means that an is a times r to the n minus 1.
00:08
For n is equal to 1, 2, 3, etc.
00:13
We're told that, let's see here, a1 is 2 greater than a2, because the first term exceeds the second term by 2.
00:33
So a1 is a2 plus 2.
00:37
Well, a1 is a2 is ar, a3 is ar squared.
00:46
And i'm also told that the sum of the first and second term is for thirds.
00:51
So, a .r plus ar squared, which is a2 plus a3, that is equal to for thirds.
01:00
And this was equivalent to a is equal to ar plus 2.
01:12
Well, that means then that a minus ar is equal to 2.
01:20
So if i divide ar plus ar squared by a minus ar, then i get 4 3 divided by 2.
01:32
Well, this i can cancel item a, because it's in a numerator and denominator, and i get r plus r squared over 1 minus r.
01:43
Then cross -multiplying, i get 2 times r plus, or wait, this is equal to, 4 thirds divided by 2 is 4 .6th.
02:06
So now cross -multiplying, i get 6 times r plus r squared.
02:11
Is equal to four times 1 minus r.
02:20
And of course i can divide out of 2.
02:23
This is 3 and this is 2.
02:29
So that means 3r squared plus 3r plus 2r minus 2 is equal to 0 or 3r squared plus 5r minus 2 is 0.
02:45
Then using the quadratic formula gives me r as equal to negative 5 plus or minus the square root of 5 squared, minus 4 times 3 times negative 2...