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Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

–77, –76, –75, –74, ...

Sagot :

Semsee45idn

Answer:

[tex]a_n=n-78[/tex]

Step-by-step explanation:

Given sequence:

-77, -76, -75, -74, ...

This is an arithmetic sequence as the difference between each term is the same.

General form of an arithmetic sequence

[tex]\boxed{a_n=a+(n-1)d}[/tex]

Where:

  • [tex]a_n[/tex] is the nth term.
  • [tex]a[/tex] is the first term.
  • [tex]d[/tex] is the common difference between terms.
  • [tex]n[/tex] is the position of the term.

To find the common difference (d), subtract consecutive terms:

[tex]\implies d=a_2-a_1=-76-(-77)=1[/tex]

Substitute the first term and the found common difference into the formula to create an equation for the nth term:

[tex]\implies a_n=-77+(n-1)(1)[/tex]

[tex]\implies a_n=-77+(n-1)[/tex]

[tex]\implies a_n=-77+n-1[/tex]

[tex]\implies a_n=n-78[/tex]

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