geometric sequence


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  
Choices:
A. 9
B. 3
C. 81
D. 27           
Correct Answer: D
Solution:
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

  • Sequence
  • Term
  • Common Ratio
  • Geometric Series
  • Constant