Respuesta :

We can write an Arithmetic Sequence as a rule:

                                             [tex]y_n=221-4(n-1)[/tex]

We have to find  [tex]y_ {82}[/tex] . So we have to insert 82 as [tex]n[/tex] in the formula above:

                        [tex]y_{82}=221-4(82-1) = 221-4\cdot 81=221-324 = -103[/tex]

Answer: the missing term of the sequence is - 103

Step-by-step explanation:

In an arithmetic sequence, the consecutive terms differ by a common difference. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 221

d = 217 - 221 = 213 - 217 = - 4

n = 82

We want to determine the value of the 82nd term, T82. Therefore,

T82 = 221 - 4(82 - 1)

T82 = 221 - 4 × 81

T82 = 221 - 324

T82 = - 103

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