Final answer:
The nth term of the sequence is found using the arithmetic sequence formula an = a1 + (n - 1)d. For the sequence 17, -24, -65, -106, -147, the nth term is an = 58 - 41n.
Step-by-step explanation:
To find the nth term of the given sequence 17, -24, -65, -106, -147, let's first determine the pattern of the sequence.
If we look at the differences between the terms:
- -24 - 17 = -41
- -65 - (-24) = -41
- -106 - (-65) = -41
- -147 - (-106) = -41
we see that the difference is constant and equal to -41. This indicates that the sequence is an arithmetic sequence with a common difference of -41.
The first term (a1) in the sequence is 17, and with the common difference (d) being -41, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
Plugging in the values:
an = 17 + (n - 1)(-41)
Simplify to find the nth term:
an = 17 - 41n + 41
an = 58 - 41n
So, the nth term of the sequence is an = 58 - 41n.