Determine the 54th term of the arithmetic sequence -18, -12, -6, . . .
To determine the 54th term of the arithmetic sequence -18, -12, -6, . . . we need to first find the common difference between consecutive terms.
The common difference (d) can be found by subtracting the second term from the first term:
d = -12 -(-18) = -12 + 18 = 6
Now that we know the common difference is 6, we can find the 54th term using the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n-1)d
a_54 = -18 + (54-1) * 6
a_54 = -18 + 53 * 6
a_54 = -18 + 318
a_54 = 300
Therefore, the 54th term of the arithmetic sequence -18, -12, -6, . . . is 300.
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I apologize for the mistake. Let's correct that.
We already know that the common difference (d) is 6.
To find the 54th term of the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n-1)d
Plugging in the given values:
a_54 = -18 + (54-1)*6
a_54 = -18 + 53*6
a_54 = -18 + 318
a_54 = 300
Therefore, the 54th term of the arithmetic sequence -18, -12, -6, . . . is 300.