Question

Write the next three terms of the arithmetic sequence.

6.1, –4, –9, ...
The next three terms are:
a) -14, -19, -24
b) -12, -15, -18
c) -11, -16, -21
d) -10, -14, -19

Answer 1

To determine the next three terms of the arithmetic sequence 6.1, -4, -9, calculate the common difference and subtract it from the last known term. The common difference is -5, leading to the next terms being -14, -19, and -24.

Step-by-step explanation:

To find the next three terms of the arithmetic sequence 6.1, -4, -9, we need to determine the common difference between the terms. The difference between the first term and the second term is -4 - 6.1 = -10.1. The difference between the second and the third term is -9 - (-4) = -5. Since this is an arithmetic sequence, these differences should be consistent. We can observe that the actual consistent difference is -5, because the difference between the first and second term, when taken as -10.1, does not correctly describe an arithmetic sequence as it would create discrepancies in further terms. Thus, starting from -9, subtracting -5 for each subsequent term, the next three terms would be -14 (-9 - 5), -19 (-14 - 5), and -24 (-19 - 5).

The next three terms are:

• -14
• -19
• -24