The general term for the sequence -5, 7, 19, 31 is?
- aₙ = -5 + 12(n - 1)
- aₙ = -5 + 12(n + 1)
- aₙ = -5 - 12(n - 1)
- None of these
Explanation
Let's analyze the sequence:
-5, 7, 19, 31
The differences between consecutive terms are:
7 - (-5) = 12
19 - 7 = 12
31 - 19 = 12
The sequence has a common difference of 12.
The general term for an arithmetic sequence is:
aₙ = a₁ + (n - 1)d
where a₁ is the first term (-5) and d is the common difference (12).
aₙ = -5 + (n - 1)12
aₙ = -5 + 12(n - 1)
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