Geometric Sequences

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

The common ratio (r) can be found by dividing any term in the sequence by the previous term (r = a_n / a_(n-1)).

Yes, this sequence is geometric because each term is obtained by multiplying the previous term by a common ratio.

The explicit formula for a geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

In a geometric sequence, 'r' represents the common ratio, which is the factor by which we multiply each term to get the next term.

The 4th term is a_4 = 3 * 4^(4-1) = 3 * 64 = 192.

Daisy will receive $162 on her 5th birthday.

The formula to find the nth term of a geometric sequence is a_n = a_1 * r^(n-1).

The first three terms are 5, 10, and 20.

The sum of the first n terms (S_n) of a geometric sequence is given by S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.