Question

In an arithmetic sequence of numbers a1 = -4 and a6 = 46. Which of the following is the value of a12?

Answer 1

a₁₂ = 106

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

Answer 2

`a_(12)=106`

Explanation:

Arithmetic sequence

General form of an arithmetic sequence:
`a_n=a+(n-1)d`

where:

• 
  `a_n` is the nth term
• a is the first term
• d is the common difference between terms

Given:

• 
  `a_1=-4`
• 
  `a_6=16`

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

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

Therefore, the equation for the nth term is:

`\begin{aligned}a_n &=-4+(n-1)10\\& =10n-14 \end{aligned}`

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

`\implies a_(12)=10(12)-14=106`