Respuesta :

semsee45

Answer:

[tex]a_n=6n-13[/tex]

Step-by-step explanation:

Arithmetic sequence

General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

where:

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

Given:

  • [tex]a_1=-7[/tex]
  • [tex]a_2=-1[/tex]
  • [tex]a_3=5[/tex]
  • [tex]a_4=11[/tex]

To find the common difference, subtract consecutive terms:

[tex]\implies d=a_4-a_3=11-5=6[/tex]

Therefore, the formula for the nth term is:

[tex]\implies a_n=-7+(n-1)6[/tex]

[tex]\implies a_n=-7+6n-6[/tex]

[tex]\implies a_n=6n-13[/tex]

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