00:01
This question gives us a3 and a4 asks us to find the first n equals five terms of this sequence.
00:06
This geometric sequence and geometric sequences obey this rule.
00:10
A .n equals a r to the n minus 1.
00:13
So what we're going to do is set up a system of two equations, solve it to find a and r, and then we'll be able to find a1, a2, and a5.
00:21
So our first equation is 2, which is a 3, is a r to the 3 minus 1, which is a r squared.
00:41
And our second equation is 3 equals a r to the 4 minus 1, which is a r cubed.
01:10
Number one is a r squared so we know that if we multiply this first equation by one we get the second equation so two equals three um two r equals three or r times two equals three right because look if we factor out an r here this is a r squared times r so this means r is yeah, two over three, or three over two, pardon making mistakes this morning, three over two, right? so then using the first equation, so then, and i'll just mark it in green, by this one, oops, by this one, we have two equals a times three halves squared.
02:51
So this means that this will go down, keep going down here...
