Question

If {gn} is a geometric sequenc with gn > 0 for all n is an element of natural number,then prove that {ln gn} is an arthnetic sequence

Answer 1

g = a, ar, ar^2, ar^3, ...

ln g = ln(a), ln(a) + ln(r), ln(a) + 2ln(r), ln(a) + 3ln(r), ...

so, the AS has first term = ln(a) and difference = ln(r)

Answer 2

Not clear

Answer 3

ln(gn+1) - ln (gn) = ln (gn+1/gn) = ln r. The difference between each consecutive term is a constant which is ln r. Hence, {ln gn} is arithmetic.

Answer 4

yes