Respuesta :

Answer:

a₁₂ = 106

Step-by-step explanation:

Given

  • a₁ (first term) = -4
  • a₆ = 46

Formula for nth term

  • aₙ = a₁ + (n - 1)d

Using that to expand a₆ and find d

  • a₆ = a₁ + (n - 1) d
  • 46 = -4 + (6 - 1)d
  • 50 = 5d
  • d = 10

Finding a₁₂

  • a₁₂ = a₁ + 11d
  • a₁₂ = -4 + 11(10)
  • a₁₂ = 110 - 4
  • a₁₂ = 106
semsee45

Answer:

[tex]a_{12}=106[/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=-4[/tex]
  • [tex]a_6=16[/tex]

To find the common difference (d), substitute the given values into the general formula and solve:

[tex]\begin{aligned}\implies a_6=(-4)+(6-1)d & =46\\ 5d-4 & =46\\ 5d & = 50\\ d & =10\end{aligned}[/tex]

Therefore, the equation for the nth term is:

[tex]\begin{aligned}a_n &=-4+(n-1)10\\& =10n-14 \end{aligned}[/tex]

To find the 12th term, substitute n = 12 into the equation:

[tex]\implies a_{12}=10(12)-14=106[/tex]

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