Final answer:
The nᵗʰ term of the sequence 5, -35, -75, -115, -155 can be found using the arithmetic sequence formula, resulting in -40n + 45 as the nᵗʰ term.
Step-by-step explanation:
The given sequence is 5, -35, -75, -115, -155. To find the nth term, we need to determine the pattern. The difference between consecutive terms is -40 (-35 minus 5 is -40, -75 minus -35 is -40, and so on). This indicates that the sequence is arithmetic, with a common difference of -40. To find the nth term of an arithmetic sequence, the formula is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the term number.
Using the formula, the nth term of the given sequence is:
an = 5 + (n - 1)(-40) = 5 - 40n + 40 = -40n + 45
Hence, the nth term of the sequence is -40n + 45.The given sequence is: 5, -35, -75, -115, -155. We need to determine the nth term of this sequence.
Analyze the differences between consecutive terms:
-35 - 5 = -40
-75 - (-35) = -40
-115 - (-75) = -40
-155 - (-115) = -40
We observe that the difference between consecutive terms is always -40. The nth term can be found using the formula: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference.
Using a1 = 5 and d = -40, we can substitute these values in the formula to find the nth term: an = 5 + (n-1)(-40). Thus, the nth term of the given sequence is 5 + (n-1)(-40).