Answer:
Explanation:
To find the 53rd term of the arithmetic sequence 27, 11, -5. We need to determine the common difference first. The common difference is the constant value added or subtracted between each term.
Looking at the sequence, we can see that the common difference is -16. From 27, subtracting 16 gives us 11, and subtracting 16 again gives us -5. This pattern continues throughout the sequence.
Now that we know the common difference is -16, we can use the formula to find the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference
In this case, the first term is 27 and the common difference is -16. Plugging in these values, we have:
53rd term = 27 + (53 - 1) * (-16)
Simplifying the expression, we get:
53rd term = 27 + 52 * (-16)
53rd term = 27 - 832
53rd term = -805
Therefore, the 53rd term of the arithmetic sequence 27, 11, -5 is -805.