00:01
We're being asked to find the value of x so that x plus 3, 2x plus 1, and 5x plus 2 are consecutive terms in an arithmetic sequence.
00:09
Well, if this is an arithmetic sequence, then there's a common difference to get from one term to the next, meaning that when i subtract my a sub 2 minus a sub 1 terms, that will give us our common difference, which should be the same as if i subtracted my third term minus my second term.
00:30
That should also equal my common difference.
00:33
So if i start with my a 2 term, which is 2x plus 1, and i subtract my first term, x plus 3, this should equal to d.
00:43
Well, if i distribute that negative sign, i have 2x plus 1 minus x minus 3.
00:49
Now, if i combine like terms, i have 2x minus x, which is x, and 1 minus 3, which is negative 2.
00:56
So i'm now found d is equal to x minus 2.
00:59
Now, i'm going to do the same thing with my a sub 3 minus a sub 2.
01:03
So a.
01:04
3 is 5x plus 2, minus a.
01:07
2, which is 2x plus 1, and this should equal to d...