00:01
We have a sequence where the nth term, a .n, is 1 over 2n times the log base 10 of 1 ,000 to the n.
00:08
Let's find the first five terms of this sequence.
00:10
So this sequence looks rather imposing at first, but it's not so bad once you actually plug things in because there's a very reliable pattern.
00:17
So the first term, a1, that's going to be 1 over 2 to the 1st, so just 1⁄2 times the log of 1 ,000 to the first power.
00:28
So the general rule here is the log base 10 of 1 ,000 to any power is just going to be that power times 3.
00:36
So we just have a 3 here, giving us 3 halves.
00:42
Next up, a 2, that's going to be 1 over 2 squared, so 1 over 4 times the log of 1 ,000 squared.
00:50
So that's the second power times 3 as by the pattern.
00:54
So 2 times 3 is 6...