Final answer:
The 20th term of the linear sequence (15, 7, −1, −9, −17,...) is −137, calculated using the formula for the nth term of an arithmetic sequence.
Step-by-step explanation:
The question asks us to find the 20th term of a linear sequence. To start, we should determine the common difference between the terms. By analyzing the sequence (15, 7, −1, −9, −17), we can see that each term decreases by 8 compared to the previous term. Hence, the common difference is −8.
Now, to find the 20th term, we can use the formula for any term of an arithmetic sequence, which is:
An = A1 + (n − 1) × d
Where An is the nth term, A1 is the first term, n is the term number, and d is the common difference.
For this sequence:
- A1 = 15 (the first term)
- d = −8 (the common difference)
- n = 20 (the term number)
Plugging these values into the formula gives us:
A20 = 15 + (20 − 1) × (−8)
Which simplifies to:
A20 = 15 + 19 × (−8)
A20 = 15 − 152
A20 = −137
Therefore, the 20th term of the given linear sequence is −137.