Answer:
a = 10
T8 = 1280
Step-by-step explanation:
The nth term of a GP is expressed as;
Tn = ar^n-1
Forth term T4 = ar^3
first term = a
If the ratio of the fourth to the first term of a geometric sequence is ⅛ then;
ar^3/a = 1/8
r^3 = 1/8
r = ∛1/8
r = 1/2
If the first term exceed the second by 5, then;
a = 5 + T2
a = 5 + ar
a = 5 + a(1/2)
a-1/2a = 5
1/2 a 5
a = 10
Hence the first term is 10
T8 = ar^7
T10 = 10(1/2)^7
T10 = 10(128)
T10 = 1280
Hence the 8th term is 1280
