Answer:

A geometric progression, also known as a geometric sequence, is an ordered list of numbers in which each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio

r

. For example, the sequence

2

,

6

,

18

,

54

,

⋯

is a geometric progression with common ratio

3

. Similarly

10

,

5

,

2.5

,

1.25

,

⋯

is a geometric sequence with common ratio

1

2

.

Thus, the general form of a geometric sequence is:

a

,

a

r

,

a

r

2

,

a

r

3

,

a

r

4

,

⋯

The

n

th term of a geometric sequence with initial value

a

and common ratio

r

is given by

a

n

=

a

r

n

−

1

Such a geometric sequence also follows the recursive relation:

a

n

=

r

a

n

−

1

for every integer

Step-by-step explanation:

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