Final answer:
To find the nᵗʰ term of the sequence 18, 16, 14, 12, 10, we identify it as an arithmetic sequence with a common difference of -2. The formula for the nᵗʰ term is Tₙ = a + (n - 1)d, which yields Tₙ = 20 - 2n for this particular sequence.
Step-by-step explanation:
To find the nᵗʰ term of the given sequence 18, 16, 14, 12, 10, we first need to determine the pattern in the sequence. We can see that each term decreases by 2. This indicates that the sequence is an arithmetic sequence with a common difference d of -2.
The nᵗʰ term of an arithmetic sequence is given by the formula Tₙ = a + (n - 1)d, where a is the first term, d is the common difference, and n is the term number.
For this sequence, a is 18 (the first term) and d is -2. Plugging these values into the formula, we get:
Tₙ = 18 + (n - 1)(-2) = 18 - 2n + 2 = 20 - 2n.
So the nᵗʰ term of the sequence is 20 - 2n.
The given sequence is 18, 16, 14, 12, 10. To determine the nth term of this sequence, we can observe that each term is 2 less than the previous term. So, the pattern is:
18, 16, 14, 12, 10, ...
We can see that the first term is 18. In general, the nth term can be found using the formula:
nth term = first term - (n-1)*2
Substituting the values, we get:
nth term = 18 - (n-1)*2
Therefore, the nth term of the given sequence is 18 - (n-1)*2.