Final answer:
The nᵗʰ term of the arithmetic sequence 10, 9.98, 9.96, 9.94, 9.92 can be found using the formula an = a1 + (n - 1)d. Substituting a1 = 10 and d = -0.02 into the formula yields an = 10.02 - 0.02n.
Step-by-step explanation:
The sequence given is 10, 9.98, 9.96, 9.94, 9.92. Observing the pattern, we can see that each term is decreasing by 0.02 from the previous term. This indicates that the sequence is an arithmetic sequence, where each term is equal to the first term minus the common difference times the position minus one.
To find the nᵗʰ term of the sequence, we use the formula for the nᵗʰ term of an arithmetic sequence, which is:
an = a1 + (n - 1)d
Where an is the nᵗʰ term, a1 is the first term, n is the term number, and d is the common difference between the terms.
For this sequence:
- a1 = 10 (the first term)
- d = -0.02 (the common difference)
Therefore, to find an:
an = 10 + (n - 1)(-0.02)
Simplifying:
an = 10 - 0.02n + 0.02
Finally:
an = 10.02 - 0.02n
This is the formula for the nᵗʰ term of the given sequence.