Final answer:
The nᵗʰ term of the arithmetic sequence is 29n - 19, by using the formula for the nth term of an arithmetic sequence and plugging the values from the given sequence.
Step-by-step explanation:
The sequence given is 10, 39, 68, 97, 126. To determine the nᵗʰ term of this sequence, we need to find the pattern. Looking closely, each term increases by 29. Therefore, the sequence is arithmetic, and we can 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, d is the common difference, and n is the term number.
To find the nth term for the given sequence:
- The first term a1 is 10
- The common difference d is 29
- We plug these values into the formula:
an = 10 + (n - 1) × 29
Now, if we simplify it, we get:
an = 10 + 29n - 29
an = 29n - 19
Therefore, the nth term of the sequence is 29n - 19.