Final answer:
The nᵗʰ term for the given arithmetic sequence 20, 19, 18, 17, 16, which decreases by 1, is found using the formula Tₙ = 21 - n.
Step-by-step explanation:
The sequence given is 20, 19, 18, 17, 16 and it is a decreasing arithmetic sequence where each term decreases by 1. To find the nᵗʰ term of the sequence, we use the arithmetic series formula:
Tn = a + (n - 1)d
Where Tn is the nᵗʰ term, a is the first term, n is the term number, and d is the common difference between the terms.
For our sequence, a = 20 and d = -1 because it decreases by 1 each time.
Plugging the values into the formula, we get:
Tn = 20 + (n - 1)(-1)
Tn = 20 - n + 1
Tn = 21 - n
Therefore, the formula for the nᵗʰ term of the given sequence is 21 - n.
The given sequence is 20, 19, 18, 17, 16. To determine its nth term, we need to find a pattern in the sequence. In this case, we can see that each term is decreasing by 1. So, we can express the nth term as 20 - (n-1), where n is the position of the term in the sequence. Simplifying this expression, we get the nth term as 21 - n.