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Answer:
To find the three means between -4 and 16, we first need to determine the arithmetic mean of these two numbers. The arithmetic mean is calculated as follows:
\[ \text{Arithmetic mean} = \frac{a + b}{2} \]
where \( a = -4 \) and \( b = 16 \). Plugging in these values:
\[ \text{Arithmetic mean} = \frac{-4 + 16}{2} = \frac{12}{2} = 6 \]
So, the arithmetic mean of -4 and 16 is 6. Now, to find the three means between -4 and 16, we can use the arithmetic progression (AP) formula:
\[ \text{Terms of AP} = a, a+d, a+2d, a+3d, \ldots \]
where \( a \) is the first term and \( d \) is the common difference. Here, the first term \( a = -4 \), the fourth term \( a+3d = 16 \), and the third term should be the first mean