Question

what are arithmetic and geometric series ? with exmples ​

Answer 1

Answer:

If you have the sequence 2, 8, 14, 20, 26, then each term is 6 more than the previous term. This is an example of an arithmetic progression (AP) and the constant value that defines the difference between any two consecutive terms is called the common difference.

Step-by-step explanation:

Answer 2

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Arithmetic Progressions

If you have the sequence 2, 8, 14, 20, 26, then each term is 6 more than the previous term. This is an example of an arithmetic progression (AP) and the constant value that defines the difference between any two consecutive terms is called the common difference.

If an arithmetic difference has a first term a and a common difference of d, then we can write

a, (a + d), (a + 2d),... {a + (n-1) d}

where the nth term = a + (n−1)d

Geometric Progressions

If you have a sequence such as: 81, 27, 9, 3, 1, 1/3, 1/9,... then each term is one third of the term before.

This can be written as 81, 81(1/3), 81(1/3)2, 81(1/3)3, 81(1/3)4,...

It is an example of a Geometric Progression (GP) where the each term is a multiple of the previous one. The multiplying factor is called the common ratio.

So a GP with a first term a and a common ratio r with n terms, can be stated as

a, ar, ar2, ar3, ar4...arn-1 , where the nth term = arn-1

Example:

In the sequence, 400, 200, 100, 50,... find the 8th term.

a = 400, r = 0.5 and so the 8th term = 400 × 0.57 = 3.125

Note: To find which term has a certain value you will need to use logarithms.

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