Question

442
V 24.42
0400
0.4.0.0.42
The terms in two positions of some arithmetic sequences are given below
While the first five terms of eacy
3 term 34
3 term 43 m) 3 term 2
term 67
6 term 76
5 term 3
v 2 terms
5 term 2
be erm of an arithmetic sequence is 38 and the term is 66 .
Chris 25 term?​

Answer 1

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,

a1=1a2=a1+2=1+2=3a3=a2+2=3+2=5a4=a3+2=5+2=7a5=a4+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:

a2=a1+da3=a2+d=(a1+d)+d=a1+2da4=a3+d=(a1+2d)+d=a1+3da5=a4+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

In fact, any general term that is linear in n defines an arithmetic sequence.