00:01
Hi there, in this question, we need to just find a formula for the nth term of each sequence.
00:07
So in part a, the sequence is given as 1 over 1, and the next one is negative 1 over 8, sorry.
00:15
And the next one is 1 over 3.
00:17
So what we have to do, if you look at, i mean, this is 1 over 27, sorry, my bad.
00:23
So what kind of relation that we can see? so 2 is the third term of 2, which is 2 to the power 3.
00:34
And this one is 3 to the power 3.
00:37
And this is 1 to the power 3.
00:41
So we can just define as this is equal to.
00:46
So the first term at the top of the denominator, we got 1.
00:50
And for the second one, this is negative 1.
00:53
And the next one, which is 1.
00:54
So we can define the top of the fraction as this is, negative 1 to the power which is let's say this is 2n minus 1 and in the denominator we got 1 to the power to the power so if you plug in 1 which is n to the power 3 so this is the general formula for this function and for this sequence let me just try for n is equal to 1 which is negative 1 to the power 1 divided by 1 to the power 3 which is 1 which is negative 1 i am sorry, that should be plus.
01:32
Okay, let me try in this way.
01:36
This is 2.
01:36
Negative 1 to the second, which is 1 over 1.
01:39
So this is the first term...