Question

Find the nth term rule for the arithmetic sequence with

ay = -17 and a25 = -71.
a)an = n +4
b)an = -n + 5
c)an = -3n +4.
d)an = 3n - 2

Answer 1

To find the nth term rule for the arithmetic sequence, calculate the common difference (d) with the two given terms, use the common difference to solve for the first term, and then express the nth term using the formula 'an = a1 + (n - 1)d'.

Step-by-step explanation:

The question asks us to find the nth term rule for an arithmetic sequence given two terms: ay = -17 and a25 = -71. First, we must find the common difference (d) of the sequence. Since the difference between the indices of the two given terms (25 - y) and the difference between the values of the terms (-71 - (-17)) must be consistent with d, we can set up the equation:

d = (-71 + 17) / (25 - y)

Solving for d gives us d = -54 / (25 - y). We can then use either ay = -17 or a25 = -71 to solve for the first term (a1) of the sequence.

For ay = -17, we get -17 = a1 + (y - 1)d. Substituting the value of d from the first equation and solving for a1 will give us the initial term. Once we have a1 and d, the nth term rule, which has the form 'an = a1 + (n - 1)d', can be determined.