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 $m$?

6 possible integers

Step-by-step explanation:

Given

A decreasing geometric sequence

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

The next will be;

The nth term will be

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

then must be a proper fraction;

This implies that:

Where 7 is the denominator

The sets of is and their are 6 items in this set

Hence, there are 6 possible integer

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d