Question

In a geometric sequence where r > 1, the terms always increase.. . True or False??.

Answer 1

Answer: Hello mate!

a geometric sequence is of the form

a∑r^n = a + ar + ar^2 + ar^3..... and so on.

then if r is a number bigger than 1, the therm r^n only increases when n increases, which means that the terms in this sequence are always increasing, because r^n < r^(n+1)= r*(r^n), here you use that r > 1 to prove that r^n < r(r^n)

This means that the statement is true.

Answer 2

It is absolutely correct to say that in a geometric sequence where r > 1, the terms always increase. The correct option among the two options that are given in the question is the first option. I hope that this is the answer you were looking for and it has come to your help.