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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.
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:
- 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}, ...
- 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...
Jan 18, 2024 · The geometric sequence calculator finds the nᵗʰ term and the sum of a geometric sequence (to infinity if possible).
The geometric sequence explicit formula is: a_{n}=a_{1}(r)^{n-1} Where, a_{n} is the n th term (general term) a_{1} is the first term. n is the term position. r is the common ratio. The explicit formula calculates the n th term of a geometric sequence, given the term number, n. You create both geometric sequence formulas by looking at the ...
Find The Formula For A Geometric Sequence Given Terms. This video explains how to find the formula for the nth term of a given geometric sequence given three terms of the sequence. Example: 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, …. Show Video Lesson.
