Question

Insert five arithmetic means between 0 and -12.

A) -2, -4, -6, -8, -10
B) -1, -3, -5, -7, -9
C) -3, -5, -7, -9, -11
D) -2, -4, -6, -8, -10, -12

Answer 1

To insert five arithmetic means between 0 and -12, we calculate the common difference 'd' and determine the arithmetic sequence. The common difference is found to be -2 and the resulting arithmetic sequence is -2, -4, -6, -8, -10, which corresponds to option A.

Step-by-step explanation:

To insert five arithmetic means between 0 and -12, we need to find a sequence of numbers starting with 0 and ending with -12, where each number is an equal distance apart from the next. In an arithmetic sequence, this distance is known as the common difference 'd'.

The formula for the nth term an of an arithmetic sequence is:

an = a1 + (n - 1)d

Here, a1 is the first term and a7 is the (5 + 2)th term, which is -12. We can set up the equation to find d:

-12 = 0 + (7 - 1)d

-12 = 6d

d = -2

Now we can find the five arithmetic means:

1. -2 (0 + 1(-2))
2. -4 (0 + 2(-2))
3. -6 (0 + 3(-2))
4. -8 (0 + 4(-2))
5. -10 (0 + 5(-2))

Therefore, the correct answer is option A) -2, -4, -6, -8, -10.