Mathematics: Describe and explain the difference between explicit formulas for arithmetic sequences and explicit formulas for geometric sequences.

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Describe and explain the difference between explicit

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slonzyy1682

03.02.2022

Mathematics

Arithmetic sequence: $a_{n}=a_{1}+(n-1)d$

Geometric sequence: $a_{n}=a_{1}(r)^{n-1}$

Step-by-step explanation:

The arithmetic sequence: is the sequence whos terms increased or decreased by a constant amount.

Examples:

4, 7, 10, 13, 16, ........................ (increased by 3)25, 20, 15, 10, ......................... (Decreased by 5)

The explicit formula for the nth term of the arithmetic sequence is:

$a_{n}=a_{1}+(n-1)d$ $a_{1}$ is the first termd is the constant difference between each two consecutive termsn is the position of the number in the sequence

The geometric sequence: is the sequence whos consecutive terms have a constant ratio

Examples:

1, 2, 4, 8, 16, ........................ (Multiplying by 2)625, 125, 25, 5, ......................... (Dividing by 5)

The explicit formula for the nth term of the geometric sequence is:

$a_{n}=a_{1}(r)^{n-1}$ $a_{1}$ is the first termr is the constant ratio between each two consecutive termsn is the position of the number in the sequence

* Arithmetic sequence →→→→→→ Geometric sequence

Has a constant difference →→→→→→ Has a constant ratio

$a_{n}=a_{1}+(n-1)d$ →→→→→→ $a_{n}=a_{1}(r)^{n-1}$

$d=a_{n}-a_{n-1}$ →→→→→→ $r=\frac{a_{n}}{a_{n-1} }$

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Describe and explain the difference between explicit formulas for arithmetic sequences and explicit formulas for geometric sequences.

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