Final answer:
The nth term of the sequence 14, 64, 114, 164, 214 is found using the arithmetic sequence formula, which yields the nth term as 50n - 36.
Step-by-step explanation:
To determine the nth term of the given sequence 14, 64, 114, 164, 214, we need to identify the pattern in the sequence. We notice that each term increases by 50. So, we can conclude that the sequence is an arithmetic sequence with a common difference (d) of 50. The first term (a1) of the sequence is 14. Using the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, we can find the nth term.
Let's substitute the known values into the formula:
an = 14 + (n - 1) × 50
an = 14 + 50n - 50
an = 50n - 36
Therefore, the nth term of the sequence is 50n - 36.