What is the 32nd term of the arithmetic sequence where a1 = -31 and a9 = -119?
Solution:
The nth term of an arithmetic sequence is given by an = a + (n - 1)d.
Given the first term a = a1 = -31
common difference = d = unknown
To find the common difference substitute in the formula, we get
a9 = -119
⇒ a + (9 - 1)d = -119
⇒ a + 8d = -119
We know a = -31
⇒ -31 + 8d = -119
⇒ 8d = -119 + 31
⇒ 8d = -88
⇒ d = -11
Now, find a32
a32 = a + (32 - 1)d
a32 = -31 + (32 - 1) × (-11)
a32 = -31 + 31 × (-11)
a32 = -31 + ( -341)
a32 = -372
Therefore, the value of a32 = -372.
What is the 32nd term of the arithmetic sequence where a1 = -31 and a9 = -119?
Summary:
The 32nd term of the arithmetic sequence where a1 = -31 and a9 = -119 is a32 = -372.
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