Question

find the general term (un), of the geometric sequence which has :

u7=24 and u15= 384


thank u

Answer 1

The ratio of u15 and u7 is 16, which is 2^4
The term number (n) change from u7 to u15 is 8. A factor of 16 change would result from each term being higher by 2^(1/2) or sqrt2.

So try un = C*2^(n/2)

Evaluate C as follows:
When n = 7
24 = C*2^(7/2)
24 = C*8 sqrt2. Therefore
C = 3/sqrt2

un = (3/sqrt2)*2^(n/2)

Check: u15 = [3/2^(1/2)]*2^15/2
= 3* 2^7 = 384

It works

Answer 2

Ops