Final answer:
The nᵗʰ term of the given sequence is represented by the linear expression 37 - 30n.
Step-by-step explanation:
To find the nᵗʰ term of the given sequence 7, -23, -53, -83, -113, we first need to determine the pattern of the sequence. We observe that each term is decreasing by 30 from the previous term. This indicates a linear relationship, thus the nᵗʰ term can be expressed as an + b, where a is the common difference and b is the first term of the sequence.
Calculating the common difference, we have:
- Common difference (a) = -23 - 7 = -30
Since the first term is 7, we can now write the formula for the nᵗʰ term:
- nᵗʰ term = 7 + (n - 1)(-30)
Simplifying this, we get:
- nᵗʰ term = 7 - 30n + 30
- nᵗʰ term = 37 - 30n
The nᵗʰ term of the sequence is 37 - 30n.
To find the nᵗʰ term of the sequence 7, -23, -53, -83, -113, we can observe that each term is decreasing by 30. Therefore, we can find the nᵗʰ term by subtracting 30 from the previous term. Let's consider the first term, 7. To find the second term, we subtract 30 from 7: 7 - 30 = -23. To find the third term, we subtract 30 from -23: -23 - 30 = -53. We can continue this pattern to find any term in the sequence.