James10492
Junior Member
- Joined
- May 17, 2020
- Messages
- 50
This came up from a problem involving a fairly simple geometric sequence
40, -20, 10, -5...
the first term in the sequence is 40
the common ratio is -.5 (-1/2)
so the nth term of the sequence can be given by 40 x -.5n-1
now, it turns out you can write this as (-1)n-1 x 5/2n-4
40 x .5n-1 = 5 x 8 x -.5n-1
=5 x 23 x -.5n-1
.5 = 2-1 , so
5 x 23 x (-2-1)(n-1)
= 5 x 23 x -21-n
= -1 x 5 x 23 x 2(1-n)
now 23 x 21-n = 24-n, which gives you your 1/2(n-4)
but now I am stuck - I don't see how -5 x 1/2(n-4) = (-1)n-1 x 5/2n-4
40, -20, 10, -5...
the first term in the sequence is 40
the common ratio is -.5 (-1/2)
so the nth term of the sequence can be given by 40 x -.5n-1
now, it turns out you can write this as (-1)n-1 x 5/2n-4
40 x .5n-1 = 5 x 8 x -.5n-1
=5 x 23 x -.5n-1
.5 = 2-1 , so
5 x 23 x (-2-1)(n-1)
= 5 x 23 x -21-n
= -1 x 5 x 23 x 2(1-n)
now 23 x 21-n = 24-n, which gives you your 1/2(n-4)
but now I am stuck - I don't see how -5 x 1/2(n-4) = (-1)n-1 x 5/2n-4