Question

A particular geometric sequence has strictly decreasing terms. After the first term, each successive term is calculated by multiplying the previous term by $\frac{m}{7}$. If the first term of the sequence is positive, how many possible integer values are there for $m$?

Answer 1

Answer:

6 possible integers

Step-by-step explanation:

Given

A decreasing geometric sequence

$Ratio = \frac{m}{7}$

Required

Determine the possible integer values of m

Assume the first term of the sequence to be positive integer x;

The next sequence will be $x * \frac{m}{7}$

The next will be; $x * (\frac{m}{7})^2$

The nth term will be $x * (\frac{m}{7})^{n-1}$

For each of the successive terms to be less than the previous term;

then $\frac{m}{7}$ must be a proper fraction;

This implies that:

$0 < m < 7$

Where 7 is the denominator

The sets of $0 < m < 7$ is $\{1,2,3,4,5,6\}$ and their are 6 items in this set

Hence, there are 6 possible integer