The second and fifth term of a geometric profession are 1 and 1/8 resecitive find the common ratio, first term and eight term

Answer 1

a_5/a_2 = ar^4/ar = r^3 = 1/8
so r = 1/2
now you want a and ar^7

or, knowing r,
a = a_2/r
a_8 = a_5 * r^3

Answer 2

In geometric progression:

an = a1 ∙ q ⁿ ⁻ ¹

In this case:

a2 = 1 = a1 ∙ q

a1 ∙ q = 1

a5 = 1 / 8 = a1 ∙ q⁴

a1 ∙ q⁴ = 1 / 8

Now:

a1 ∙ q⁴ = 1 / 8

a1 ∙ q ∙ q³ = 1 / 8

Since a1 ∙ q = 1

1 ∙ q³ = 1 / 8

q³ = 1 / 8

q = ∛ ( 1 / 8 )

q = ∛1 / ∛8

q = 1 / 2

Put this value in equation:

a1 ∙ q = 1

a1 ∙ 1 / 2 = 1

Multiply both sides by 2

a1 = 2

a8 = a1 ∙ q⁷

a8 = 2 ∙ ( 1 / 2 )⁷

a8 = 2 ∙ 1⁷ / 2⁷

a8 = 2 ∙ 1 / 2⁷

a8 = 1 / 2⁶

a8 = 1 / 64

Your geometric progression:

2 , 1 , 1 / 2 , 1 / 4 , 1 / 8 , 1 / 16 , 1 / 32 , 1 / 64 ....

Answer 3

Common ratio=(1/8)/(1/4)
Common ratio=1/8*4/1
Common ratio=1/2
Sn=a(1-r^n)/1-r
S8=1/4(1-1/2)/(1-1/2)
S8=1/4(1-1/256)/1-(1/2)
S8=1/4(255/256)/1/2
S8=(255/1024)/(1/2)
S8=(255/1024)*2/1
S8=255/512.