Find the common ratio for the geometric sequence. a2 = 224 and a7 = 7

Question

a. 

r = 4

b. 

r = 2

c. 

r = 0.5

d. 

r = 0.25

Answer 1

a₇ = a₂(r)⁵

7 = 224(r)⁵

7 / 224 = r⁵

Can you calculate and answer?

Answer 2

a2 =244

a7 = 7

GP what is r?

it's a proper fraction, less than 1 about 0.49152

if r= 1/2 then the sequence would be

244, 122, 61, 30.5 15.25, 7.625, so r is slightly less than .5

a3 = a2r

a7 = a2r^5

r^5 = a7/a2 = 7/244

r = 5th root of 7/244 = about .49

Answer 3

A little more explanation:

a_n=a₁r^n-1

a₂=a₁r^2-1 ==> a₁=a₂/r

a₇=a₁r^7-1=(a₂/r)r⁶=a₂r⁵