Pre-Calculus Prep: Finding the nth Term in a Geometric Sequence
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In pre-calculus, a geometric sequence is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. To find the nth term of a geometric sequence, you need two pieces of information: the first term of the sequence (often denoted as "a") and the common ratio (often denoted as "r").
The general formula for the nth term of a geometric sequence is given by:
Term n = a * (r^(n-1))
In this formula, "n" represents the term number you want to find, "a" represents the first term of the sequence, and "r" represents the common ratio.
To find the nth term, you can substitute "n" into the formula and calculate the value. Here's an example to illustrate the process:
Consider a geometric sequence with a first term of 2 and a common ratio of 3. Using the formula mentioned above, we can find the nth term:
Term n = 2 * (3^(n-1))
So, if we want to find the 5th term of this geometric sequence, we substitute "n = 5" into the formula:
Term 5 = 2 * (3^(5-1))
= 2 * (3^4)
= 2 * 81
= 162
Therefore, the 5th term of the geometric sequence with a first term of 2 and a common ratio of 3 is 162. You can use the same formula to find the nth term for any term number in the geometric sequence by substituting the corresponding value for "n".
These videos are designed to review and reteach Precalculus and Collegeboard Pre-CALC AP content. My videos cover functions, polynomials, exponential and logarithmic expressions, trigonometry, parametric equations, polar coordinates, vectors, matrices and systems, conic sections, discrete mathematics, sequences and series; and an introduction to calculus.
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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa .
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