Final answer:
To insert four arithmetic means between -1 and -3.5, we calculate the common difference (d = -0.625) and successively add this to the first term, resulting in the means: -1.625, -2.25, -2.875, and -3.5.
Step-by-step explanation:
To insert four arithmetic means between -1 and -3.5, we first need to determine the common difference (d) used in the arithmetic sequence. The formula for the nth term of an arithmetic sequence is: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, and d is the common difference. This situation requires us to find the fifth term since it must be equal to -3.5 (the last number in the sequence) while -1 is the first term (a1).
The sequence has a total of 6 terms (including the first and the last numbers) and thus 5 gaps between them, so the formula for the fifth term is: -3.5 = -1 + (5 - 1)d, which simplifies to -2.5 = 4d, giving us a common difference of d = -0.625. Now we can find the four arithmetic means between -1 and -3.5 by adding the common difference to -1 successively.
The first arithmetic mean is -1.625, the second is -2.25, the third is -2.875, and the fourth is -3.5. Hence, the four arithmetic means between -1 and -3.5 in the arithmetic sequence are -1.625, -2.25, -2.875, and -3.5.