Question

A sequence is generated by the formula Mn =an² + bn+c, where a , b and c are constants. If M.1 = 4, M2 = 10 and M3 = 18, find the values of a b and c.

Answer 1

The constants a, b, and c in the sequence formula Mn = an² + bn + c given M1 = 4, M2 = 10, and M3 = 18 are a = 1, b = 1, and c = 2 respectively.

Step-by-step explanation:

The sequence is generated by the formula Mn = an² + bn + c, where a, b, and c are constants. Given that M1 = 4, M2 = 10, and M3 = 18, this forms a system of equations which are as follows:

• For M1 = 4, n=1: a(1)² + b(1) + c = 4,
• For M2 = 10, n=2: a(2)² + b(2) + c = 10,
• For M3 =18, n=3: a(3)² + b(3) + c = 18.

So we have three equations: a + b + c = 4, 4a + 2b + c =10, 9a + 3b + c = 18. By solving this system of linear equations, we find that a = 1, b = 1, and c = 2.

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