Explicit Formula for Geometric Sequence
The explicit formula for a geometric sequence is given by the equation:
An = A1 * r^(n-1)
Where:
– An represents the nth term of the sequence
The explicit formula for a geometric sequence is given by the equation:
An = A1 * r^(n-1)
Where:
– An represents the nth term of the sequence.
– A1 represents the first term of the sequence.
– r represents the common ratio of the sequence.
– n represents the position of the term within the sequence.
To find any term in a geometric sequence, simply substitute the values of A1, r, and n into the formula.
For example, let’s say we have a geometric sequence where A1 = 2 and r = 3.
To find the 5th term (An) of the sequence, we can use the formula:
A5 = 2 * 3^(5-1)
= 2 * 3^4
= 2 * 81
= 162
Therefore, the 5th term of the sequence is 162.
It’s important to note that the common ratio (r) should not be zero, as dividing by zero is undefined. Additionally, if the common ratio (r) is negative, the terms of the sequence will alternate in sign (positive and negative).
More Answers:
The Explicit Formula for Arithmetic Sequences | How to Find Any Term by Plugging in the PositionThe Importance of Understanding the Common Ratio in Geometric Sequences and Progressions
The Sum of an Infinite Geometric Series | A Step-by-Step Guide