A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

A sequence where each term is added to the previous one by a constant.

A sequence where each term is subtracted from the previous one by a constant.

A mathematical series where numbers are arranged in increasing order.

By adding the first and last term.

By multiplying any term by the previous term.

By subtracting any term from the previous term.

By dividing any term by the previous term.

a_n = a_1 * r^(n-1) where a_1 is the first term and r is the common ratio.

a_n = a_1 * (n-1) + r.

a_n = n * a_1 - r.

a_n = a_1 + r^(n-1).

S_n = a * (1 - r^n) / (1 - r) for r ≠ 1.

S_n = a * n * r.

S_n = a_n + r^n.

S_n = a + r + n.

12

24

18

16

In a geometric sequence, each term is multiplied by a constant ratio, whereas in an arithmetic sequence, a constant is added to each term.

In a geometric sequence, each term is subtracted by a constant, whereas in an arithmetic sequence, a constant is added to each term.

A geometric sequence involves division; an arithmetic sequence involves multiplication.

In a geometric sequence, each term is multiplied by a variable, whereas in an arithmetic sequence, a constant is added.

5

3

15

9

The sequence decreases to zero.

The sequence remains constant, with each term equal to the first term.

The sequence alternates between 1 and -1.

The sequence becomes an arithmetic series.

1/2

2

1

1/4

A geometric series that has an infinite number of terms.

A geometric series with a finite number of terms.

A sequence with both geometric and arithmetic properties.

A sequence with alternating common ratios.

When the common ratio is greater than 1.

When the terms increase exponentially.

It converges when the absolute value of the common ratio is less than 1.

It converges if it is finite.

S = a / (1 - r) for |r| < 1.

S = a * (1 - r)^(n-1).

S = ar^n / (1 - r).

S = a + r + n.

First term is 10, common ratio is 4.

First term is 10, common ratio is -2.

First term is -10, common ratio is 2.

First term is 20, common ratio is -1.

First term a_1 = 128 / 2^(6-1) = 4.

First term a_1 = 2 * 128 = 256.

First term a_1 = 32.

First term a_1 = 128 / 6 = 21.33.

True, with a common ratio of 3.

False, with a common difference of 2.

True, with no pattern.

False, it is an arithmetic sequence.