Final answer:
To find the sum of M1, M3, M5, and M7, we need to find the constant d by analyzing the given sequence. Each term in the sequence is equal to the succeeding term minus a constant. We can express each term in terms of M2 and then find the sum. The sum of M1, M3, M5, M7 is 192 + 4d.
Step-by-step explanation:
To find the sum of M1, M3, M5, and M7, we need to understand the pattern in the given sequence.
From the given sequence, each term is equal to the succeeding term minus a constant. Let's find the constant, d.
We know that M2 + M4 + M6 = 48. Therefore, M4 = 48 - M2 = 48 - (M2 - d) = 48 - M2 + d.
We can also express M4 as M4 = M2 + d. Applying the same logic, we can express M6 as M6 = M4 + d = M2 + 2d.
So, M6 = M2 + 2d = 48.
From this, we can find the value of M2.
Solving the equation M2 + 2d = 48, we get M2 = 48 - 2d.
Now, to find the sum of M1, M3, M5, and M7, we can express each term in terms of M2. We have M3 = M2 + 2d = 48, M5 = M2 + 4d, and M7 = M2 + 6d.
Sum of M1, M3, M5, M7 = M1 + M3 + M5 + M7 = M2 + (M2 + 2d) + (M2 + 4d) + (M2 + 6d).
Plugging in the value of M2 = 48 - 2d, we get the final expression for the sum: Sum = M2 + (M2 + 2d) + (M2 + 4d) + (M2 + 6d) = (48 - 2d) + (48 - 2d + 2d) + (48 - 2d + 4d) + (48 - 2d + 6d) = 4M2 + 12d = 4(48 - 2d) + 12d = 4(48) - 8d + 12d = 192 + 4d.
Therefore, the sum of M1, M3, M5, M7 is 192 + 4d.