Series And Sequence (1 Viewer)

[ghostman_on_3rd]

Hi, I forgot how you do these type of questions again.

Find the smallest term of the sequence 400, 200, 100,..... which is greater than 3

Thanks in advance!

 

[Drongoski]

The 8th term = 400 x (1/2)^(8-1) = 3.125

 

[ghostman_on_3rd]

The 8th term = 400 x (1/2)^(8-1) = 3.125

True, but how did you work out N is 8?

 

[Aplus]

Make it an inequality.
T_n > 3

 

[ghostman_on_3rd]

oh, i see, thanks

 

[Drongoski]

Well here you have a G.P.

n-th term T_n = 400 x (1/2)^n-1
You can do it the rough & easy way or the one involving inequalities.
Via rough & ready: set 400 x (1/2)^n-1 = 3 and solve for n

You get n-1 = ln(400/3) /ln 2 = 7.058 ... ==> n = 8.058 .. ==> smallest n = 8

If unsure can always find T_n for n = 8 and for n = 9
It's a brute force method but easier for some people