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Finding the n th Term of a Geometric Sequence. Given a geometric sequence with the first term a 1 and the common ratio r , the n th (or general) term is given by. a n = a 1 ⋅ r n − 1 . Example 1: Find the 6 th term in the geometric sequence 3 , 12 , 48 , ... . a 1 = 3 , r = 12 3 = 4 a 6 = 3 ⋅ 4 6 − 1 = 3 ⋅ 4 5 = 3072. Example 2:
- Sigma Notation of a Series
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- Sigma Notation of a Series
- continuing a geometric sequence. Calculate the next three terms for the geometric progression 1, 2, 4, 8, 16, … Take two consecutive terms from the sequence.
- continuing a geometric sequence with negative numbers. Calculate the next three terms for the sequence -2, -10, -50, -250, -1250, … Take two consecutive terms from the sequence.
- continuing a geometric sequence with decimals. Calculate the next three terms for the sequence 100, 10, 1, 0.1, 0.01, … Take two consecutive terms from the sequence.
- continuing a geometric sequence involving fractions. Calculate the next three terms for the sequence. 10, \quad 5, \quad 2\frac{1}{2}, \quad 1 \frac{1}{4}, \quad \frac{5}{8}, ...
Mar 27, 2022 · We will be using the general rule for the nth term in a geometric sequence and the given term (s) to determine the first term and write a general rule to find any other term. Let's consider the geometric sequence in which the common ratio is − 45 and a5 = 1280.
Learn about and revise how to continue sequences and find the nth term of linear and quadratic sequences with GCSE Bitesize AQA Maths.
This video explains how to find the formula for the nth term of a given geometric sequence given three terms of the sequence. Given the information about the geometric sequence, determine the formula for the nth term. a 0 = 5, a 1 = 40/9, a 3 = 320/81, ….
Master how to use the Geometric Sequence Formula, learn how to generate a geometric sequence, and compute the nth term of the geometric sequence. Calculate the fixed quotient and understand how every term is generated using a common ratio.
Jan 18, 2024 · To find the nth term of a geometric sequence: Calculate the common ratio raised to the power (n-1). Multiply the resultant by the first term, a.
