What is the mean of four consecutive even integers \(a\) , \(b\) , \(c\) , \(d\) ? \(a\) is the smallest integer among these.
1. \(a + d = b + c\)
2. \(b + c = d - a\)
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It is assumed that "a" is the first term in this sequence.
"a", however can be the first and the last term in the sequence. This is not specified in the question stem. Then answer is E.
If, "a" = first term, then we have b+c = d-a, a is first term then d is last and d = a+6, so d-a = 6. From there we find the sequence to be equal to a = 0, b = 2, c = 4, d = 6.
If, "a" = last term, then we have b+c = d-a, a is last term then d is first and d = a-6, so d-a = -6. From there we find the sequence to be equal to d = -6, b = -4, c = -2, a = 0.
a, b, c, d = 0, 2, 4, 6
d, b, c, a = -6, -4, -2, 0.
They both satisfy S1 and S2 but their means are 3 and -3 respectively. So unless we know what the first term of the sequence, "a" or "d" is, we can't define the mean.
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