# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-numbers-Geomtetric%20Sequences.html


## Geometric sequences

"Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them." — Joseph Fourier


#### Geometric Sequences


##### What you have to know :

- You must be able to manipulate algebraic expressions (If not, check this lesson)
- You must be able to manipulate exponential expressions. (If not, check this lesson)
- You must be able to solve simultaneous equations. (If not, check this lesson)

##### Key Points

- 1. Watch the video:
- 2. Read this presentation
- 3. Watch this solved problem

#### Extra


##### Material and references:

- Hodder Book SL(ISBN: 9781510462359) : 2B

##### Key Points

- 1. You should know the formula for the \( n \)th term of a geometric sequence: \[ u_n = u_1 r^{\,n-1}. \]
- 2. You should know the two versions of the formula for the sum of the first \( n \) terms of a geometric sequence: \[ S_n = \frac{u_1(1 - r^n)}{1 - r}, \quad r \ne 1 \] or \[ S_n = \frac{u_1(r^n - 1)}{r - 1}, \quad r \ne 1. \]

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