Thread: geometric Sequence

(b) Consider the following geometric sequence.

400

,

320

,

256

,

204

.8,

...

(i)

Write down a recurrence system that describes this sequence.

(Denote the sequence by

xn,and itsfirsttermby x1.)

[

2]

(ii) Find a closed form for this sequence.

[

2]

(iii) Use the closed form from part (b)(ii) to find the tenth term of the

sequence, giving your answer correct to four decimal places.

[

2]

note 320/400=0.8 (=256/320=...). You thus find x_n = 0.8 x_(n-1), the closed form is then given by x_n = 400*(0.8)^(n-1).
Can you do the other exercise yourself now?

Originally Posted by batman

note 320/400=0.8 (=256/320=...). You thus find x_n = 0.8 x_(n-1), the closed form is then given by x_n = 400*(0.8)^(n-1).
Can you do the other exercise yourself now?

Im not sure i understand the 320/400 part but am not sure of the formula you have given.

PLease help, thankyou so far!

You have the sequence 400, 320, 256, 204.8. Now you see that the next one is the previous one times 0.8 as 320=400*0.8, 256=320*0.8 and 204.8=256*0.8. More generally you have x_n = 0.8*x_(n-1) with x_1=400.