Write a rule for the arithmetic sequence. 5, 56, 107, 158, quickly respond                             &   75, 57, 39, 21,                             &   9  2/3, 11  1/3, 13, 14  2/ fractions

The rules for the arithmetic sequences are:

1.

2.

3.

The nth term of an arithmetic sequence is given by:

In which:

is the first term,d is the common ratio, which is the difference between consecutive terms.

1. 5, 56, 107, 158, ...

The first term is .The common difference is .

Hence, the rule is:

2. 75, 57, 39, 21, ...

The first term is .The common difference is .

Hence, the rule is:

3. 9 2/3, 11 1/3, 13, 14 2/3,...

The first term is .The common difference is .

Hence, the rule is:

A similar problem is given at link

An = a1 + (n - 1) * dthis is the arithmetic sequence formula
n = term to find
a1 = first term
d = common difference

5,56,107,158to find the common difference, subtract the 1st term from the 2nd term...(56 - 5) = 51all this is saying is that u have to add 51 to each term to find the next term.

so the rule for this one is : an = 5 + (n - 1) * 51...or it could also be written as : an = 5 + 51(n - 1)

an = a1 + (n - 1) * d
75,57,38,21

the common difference is 57 - 75 = - 18ur adding -18 to each term to find the next term.
the rule is : an = 75 + (n - 1) * -18or an = 75 - 18(n - 1)

an = a1 + (n - 1) * d

9 2/3, 11 1/3, 13,14 2/3...
the common difference is : 11 1/3 - 9 2/3 = 10 4/3 - 9 2/3 = 1 2/3

so the rule is : an = 9 2/3 + (n - 1) * 1 2/3...or an = 9 2/3 + 1 2/3(n - 1)