what is the common ratio of a geometric sequence if the first term is 8 and the 6th term is 243/128 <-- this is fraction

Question

first term is 8 and the 6th term is 243 over 128.

i can't get the common ratio.

may i ash your help?

 

Answer 1

a_n = a₁(r)^n-1

243/128 = 8(r)⁵

243/1028 = r⁵

3⁵/4⁵ = r⁵

3/4 = r

Answer 2

The terms of a geometric sequence may be written as

a, ar, ar²,...,ar^n-1 for thre first n terms

8 is the first term, 8r⁵ is the sixth term

8r⁵=243/128=3⁵/2⁷ divide by 8=2³

r⁵=3⁵/2¹⁰ and so r=3/2²=3/4