What is the 32nd term of the arithmetic sequence where a1 = 13 and a13 = –59?
errrr, assuming there is a slope...
slope = (-59 - 13)/(13-1)
slope = -6
y = -6x + c
13 = -6(1) + c
c = 19
To check
y = -6x + 19
y = -6(13) + 19
y = -59
Not sure what grade this is sorry...
To find the 32nd term of an arithmetic sequence, we need to first determine the common difference (d) between each term.
The formula to find the nth term of an arithmetic sequence is:
an = a1 + (n - 1) * d
Given that a1 = 13 and a13 = -59, we can use this information to find the common difference.
Using the formula, we substitute a1 = 13 and n = 13:
-59 = 13 + (13 - 1) * d
Simplifying the equation, we get:
-59 = 13 + 12d
Moving the terms around, we find:
12d = -72
Dividing both sides by 12 gives us:
d = -6
Now that we know the common difference (d = -6), we can use the formula to find the 32nd term, substituting a1 = 13 and n = 32:
a32 = 13 + (32 - 1) * (-6)
Simplifying the equation, we have:
a32 = 13 + 31 * (-6)
Calculating the result, we get:
a32 = 13 - 186
Therefore, the 32nd term of the arithmetic sequence is -173.