Final answer:
To find the nᵗʰ term of the given arithmetic sequence, we first calculated the common difference, then found the first term, and formulated the nᵗʰ term: Tₙ = 10 - 8n.
Step-by-step explanation:
Arithmetic sequence problems involve finding a specific term within a sequence where the difference between consecutive terms is constant. In this case, we are given the third term (-14) and the fifth term (-30) of an arithmetic sequence and must determine the nth term of the sequence.
To find the nth term, we will use the formula for an arithmetic sequence:
Tn = a + (n-1)d, where Tn is the nth term, a is the first term, and d is the common difference.
Step 1: Find the common difference (d) using the given terms. Since the sequence progresses from the third to the fifth term, there are two steps, so:
- (-30) - (-14) = -16
- d = -16 / 2 = -8
Step 2: Find the first term (a). We can use the third term for this:
- -14 = a + 2(-8)
- -14 = a - 16
- a = 2
Step 3: Write the formula for the nth term:
Tn = 2 + (n-1)(-8)
Step 4: Simplify the formula:
Tn = 2 - 8n + 8
Tn = 10 - 8n
The nth term of the sequence is 10 - 8n.