Question

the ratio of the fourth to the first term of a geometric sequence is ⅛. if the first term exceeds the second term by 5, find the first and the 8th term of the sequence?​

Answer 1

a = 10

T8 = 1280

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