Answer :
When r is an positive value then the pattern will be increased. Otherwise if the value of r is negative then the pattern will be automatically decreased.
Geometric progression:
Geometric progression means the sequence in which the ratio between any two consecutive terms is a constant.
The general form of geometric progression is,
a, ar, ar², ar³,…, arⁿ⁻¹.
where
a = First term
r = common ratio
Given,
The sequence is 5,5r,5r²,5r³.....
Here we need to find the value of r when it forms the increasing pattern and when it forms the decreasing pattern.
For example,
when we take the value of r = 2 as the positive value.
Then the sequence is like,
=> 5, (5 x 2), 5 x (2)², 5 x (2)³.....
This one is equal to,
=> 5, 10, 20, 40...….
Now, the sequence is in increasing order.
Similarly,
when we take the value of r = -2 as the negative value.
Then the sequence must be,
=> 5, 5 x (-2), 5 x (-2)², 5 x (-2)³...…
=> 5, -10, 20, -40
Now, the sequence follows the decreasing order.
To know more about Geometric Progression Here
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