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Learn about and revise how to continue sequences and find the nth term of linear and quadratic sequences with GCSE Bitesize AQA Maths.
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:
In order to generate a geometric sequence, we need to know the n^{th} term. Using a as the first term of the sequence, r as the common ratio and n to represent the position of the term, the n^{th} term of a geometric sequence is written as ar^{n-1}.
Jan 18, 2024 · The geometric sequence calculator finds the nᵗʰ term and the sum of a geometric sequence (to infinity if possible).
- How to “derive” The Geometric Sequence Formula
- Breakdown of The Geometric Sequence Formula
- Examples of Using The Geometric Sequence Formula
To generate a geometric sequence, we start by writing the first term. Then we multiply the first term by a fixed nonzero number to get the second term of the geometric sequence. To obtain the third sequence, we take the second term and multiply it by the common ratio. Maybe you are seeing the pattern now. To get to the next term of the sequence, yo...
Notes about the geometric sequence formula: 1. the common ratior cannotbe zero 2. nis the position of the term in the sequence. For example, the third term is [latex]n=3[/latex], the fourth term is [latex]n=4[/latex], the fifth term is [latex]n=5[/latex], and so on.
To learn and get familiar with the formula quickly, we will start with easy or foundational problems then gradually progress to more challenging ones. Feel free to skip the problems that you already know and jump to the ones that you want to go over. Example 1: Tell whether each sequence is geometric or not. Explain. a) Sequence A: [latex]3,12,48,1...
Dec 5, 2022 · The n th term is given by ar n-1. Simply insert the values of a, r and n in this formula and evaluate the resulting expression to get the n th term.
Calculator to identify sequence, find next term and expression for the nth term. Calculator will generate detailed explanation.
