Final answer:
To find the nth term of the sequence 14, 84, 154, 224, 294, we establish that it is an arithmetic sequence with a common difference of 70. Using the formula for the nth term of an arithmetic sequence, we determine that the nth term is 70n - 56.
Step-by-step explanation:
To determine the n term of the sequence 14, 84, 154, 224, 294, we need to identify the pattern that the sequence follows. Looking at the difference between consecutive terms, we can see that it is constant, which indicates an arithmetic sequence.
First, let's find the common difference (d) by subtracting any term from the term that follows it:
84 - 14 = 70
154 - 84 = 70
224 - 154 = 70
294 - 224 = 70
With a common difference of 70, we can conclude that d = 70.
The formula to find the nth term of an arithmetic sequence is given by:
an = a1 + (n-1)d
Where a1 is the first term of the sequence. In our case, a1 = 14.
Substituting the values we have:
an = 14 + (n-1)×70
Simplifying further:
an = 14 + 70n - 70
an = 70n - 56
Therefore, the nth term of the sequence is 70n - 56.