What is the 32nd term of the arithmetic sequence where a1 = -32 and a9 = -120?
To find the 32nd term of an arithmetic sequence, we need to determine the common difference (d) and then use the formula for the nth term of an arithmetic sequence.
First, let's find the common difference (d) using the given information about the sequence. We are told that a1 (the first term) is -32, and a9 (the ninth term) is -120.
We can use the formula for the nth term of an arithmetic sequence to find the common difference:
a9 = a1 + (9-1)d
-120 = -32 + 8d
-120 + 32 = 8d
-88 = 8d
d = -88/8
d = -11
Now that we know the common difference is -11, we can use the formula for the nth term of an arithmetic sequence to find the 32nd term (a32):
a32 = a1 + (32-1)d
a32 = -32 + 31(-11)
a32 = -32 - 341
a32 = -373
Therefore, the 32nd term of the arithmetic sequence is -373.
T9-T1 = 8d, so
8d = -120 - (-32)
8d = 88
d = 11
T32 = T1+31d
= -32 + 31(11)
= ?