(a) For some positive integer n, the expansion of (1 + x)^n has three consecutive coefficients a, b, c that satisfy a:b:c = 1:2:3. What must n be?
(b) If a:b:c = 1:8:40 and a + b + c = 100, then what is a?
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Since the ratio of a:b:c is 1:8:40, we can write a = x, b = 8x, and c = 40x.
We also know that a + b + c = 100, so we can substitute the values of a, b, and c into this equation to get:
x + 8x + 40x = 100
Combining like terms, we get 49x = 100.
Dividing both sides of the equation by 49, we get x = 2.
Therefore, the value of a is 2.