If the 3rd term in an arithmetic sequence is 9 and the common difference is -3, what is the 6th term of the sequence?
Options:
0
18
3
12
6
Answer (2)
To solve this problem, we need to find the 6th term of an arithmetic sequence given that the 3rd term is 9 and the common difference is -3.
In an arithmetic sequence, each term is generated by adding a common difference to the previous term. The formula to find the n -th term of an arithmetic sequence is:
a n = a 1 + ( n − 1 ) ⋅ d
where:
a n is the n -th term,
a 1 is the first term,
d is the common difference,
n is the term number.
Given:
The 3rd term, a 3 = 9
The common difference, d = − 3
We can use the formula to express the 3rd term:
a 3 = a 1 + 2 ⋅ d = 9
Substitute d = − 3 :
9 = a 1 + 2 ⋅ ( − 3 )
9 = a 1 − 6
Solving for a 1 , we get:
a 1 = 15
Now that we know a 1 = 15 , we can find the 6th term using the formula:
a 6 = a 1 + 5 ⋅ d
Substitute the known values:
a 6 = 15 + 5 ⋅ ( − 3 )
a 6 = 15 − 15
a 6 = 0
Therefore, the 6th term of the sequence is 0.
The correct choice is 0.
The 6th term of the arithmetic sequence is 0, calculated by first finding the first term from the 3rd term and the common difference, then using that to find the 6th term. The correct choice is 0.
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