Final answer:
To find the nth term of an arithmetic sequence with a₃ = 93 and a₆ = 108, we first calculate the common difference, then use it to find the first term and deduce the nth term formula: aₙ = 83 + (n - 1)5.
Step-by-step explanation:
The question asks us to find a formula for the nth term of an arithmetic sequence where certain terms are provided (a₃ = 93 and a₆ = 108). In an arithmetic sequence, the difference between consecutive terms (called the common difference) is constant. To find the nth term formula, we first need to calculate the common difference.
Let's denote the common difference by d and the first term by a₁. Since we know a₃ and a₆, we can say:
- a₆ = a₃ + 3d
- 108 = 93 + 3d
- 108 - 93 = 3d
- 15 = 3d
- d = 5
Now, we can use the formula for the nth term of an arithmetic sequence (aₙ = a₁ + (n - 1)d) to find a₁:
- a₃ = a₁ + 2d
- 93 = a₁ + 2(5)
- 93 = a₁ + 10
- a₁ = 83
Finally, the formula for the nth term is:
aₙ = 83 + (n - 1)5.