Final answer:
To find the nth term of the arithmetic sequence, the common difference was calculated using the provided third and fifth terms, and then the first term was obtained. The nth term is determined by the formula 14 + 60(n - 1).
Step-by-step explanation:
The question involves finding the nᵗʰ term of an arithmetic sequence given the third and fifth terms. An arithmetic sequence is a series of numbers in which the difference between consecutive terms is constant, known as the common difference (d). The formula for the nᵗʰ term of an arithmetic sequence (an) is given by:
an = a1 + (n - 1)d
Where a1 is the first term of the sequence, n is the term number, and d is the common difference. To find the common difference, we can use the given terms:
a3 = a1 + 2d = 134
a5 = a1 + 4d = 254
By subtracting the first equation from the second, we eliminate a1 and solve for d:
(a1 + 4d) - (a1 + 2d) = 254 - 134
2d = 120
d = 60
Substituting d back into the third-term equation yields a1:
a1 + 2(60) = 134
a1 = 14
Now, we can use a1 and d to find the nᵗʰ term formula:
an = 14 + (n - 1)(60)
Therefore, the nᵗʰ term of the sequence is given by 14 plus 60 times (n minus 1).