Final answer:
The n-th term of the given sequence is calculated using the arithmetic sequence formula and is found to be 70n - 59.
Step-by-step explanation:
The given sequence is: 11, 81, 151, 221, 291. To find the nth term, we need to identify the pattern. It is clear that each term increases by 70. Therefore, we have an arithmetic sequence with the first term (a1) being 11 and the common difference (d) being 70.
The formula for the nth term of an arithmetic sequence is:
an = a1 + (n - 1)d
By plugging in the values for a1 and d:
an = 11 + (n - 1) × 70
Simplify:
an = 11 + 70n - 70
an = 70n - 59
Therefore, the nth term of this sequence is 70n - 59.