Question

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Write the whole numbers in the arithmetic sequence
11 14 17
8 8 8
Do they form an arithmetic sequence?​

Answer 1

Answer:

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Answer 2

Answer:

Arithmetic Sequences

An arithmetic sequence, or arithmetic progression, is a sequence of numbers where each successive number is the sum of the previous number and some constant d.

an=an−1+d   Arithmetic Sequence

And because an−an−1=d, the constant d is called the common difference. For example, the sequence of positive odd integers is an arithmetic sequence,

1,3,5,7,9,…

Here a1=1 and the difference between any two successive terms is 2. We can construct the general term an=an−1+2 where,

a1a2a3a4a5=====⋮1a1+2=1+2=3a2+2=3+2=5a3+2=5+2=7a4+2=7+2=9

In general, given the first term a1 of an arithmetic sequence and its common difference d, we can write the following:

a2a3a4a5====⋮a1+da2+d=(a1+d)+d=a1+2da3+d=(a1+2d)+d=a1+3da4+d=(a1+3d)+d=a1+4d

From this we see that any arithmetic sequence can be written in terms of its first element, common difference, and index as follows:

an=a1+(n−1)d   Arithmetic Sequence