Definition of Geometric Sequence
- Geometric sequence is a sequence in which each term after the first term a is obtained by multiplying the previous term by a constant r, called the common ratio. It is obvious that a ≠ 0 and r ≠ 0 or 1.
1, 2, 4, 8, 16, 32, . . . is a geometric sequence.
Each term of this geometric sequence is multiplied by the common ratio 2.
More about Geometric Sequence
- Geometric series is the indicated sum of the terms of a geometric sequence.
For the geometric sequence 1, 2, 4, 8, 16, 32, 1 + 2 + 4 + 8 + 16 + 32 is the corresponding geometric series.
Solved Example on Geometric Sequence
Find the 5th term of the geometric sequence
Correct Answer: D
Step 1: In a geometric sequence, the nth term is given by an = a1 rn - 1.
Step 2: To find the fifth term, substitute n = 5 in the formula.
Step 3: The 5th term is . [Substitute and simplify.]
Related Terms for Geometric Sequence
- Common Ratio
- Geometric Series