Question

Help with sequences!
(file attached) :)

Answer 1

if the sequence below

a1, a2, a3, a4, ....

is a geometric sequence, then

a2/a1 = r
a3/a2 = r
a4/a3 = r
etc etc

for some common ratio r (ie it's a fixed number that does NOT change)

Answer 2

now apply the log to each term to get

log(a1), log(a2), log(a3), log(a4), ...

then find the difference of each term

log(a2) - log(a1) = log(a2/a1) = log(r) = d

log(a3) - log(a2) = log(a3/a2) = log(r) = d

log(a4) - log(a3) = log(a4/a3) = log(r) = d

this pattern continues

so you can see that the sequence

log(a1), log(a2), log(a3), log(a4), ...

is an arithmetic sequence