Final answer:
The nᵗʰ term of the arithmetic sequence 5, 15, 25, 35, 45 is found using the formula aₙ = 5 + (n - 1)× 10, which simplifies to aₙ = 10n - 5.
Step-by-step explanation:
To determine the nth term of the given sequence 5, 15, 25, 35, 45, we first observe the pattern. It's quickly apparent that this is an arithmetic sequence, where each term increases by 10 from the previous one. To find the nth term, use the arithmetic sequence formula:
an = a1 + (n - 1)d
where a1 is the first term of the sequence and d is the common difference between terms. In our case, a1 = 5 and d = 10. Substituting these values into the formula gives:
an = 5 + (n - 1) × 10
Simplify to get the nth term:
an = 5 + 10n - 10
an = 10n - 5
So the nth term is 10n - 5, where n represents the position of the term in the sequence.