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(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?

 Nov 9, 2023
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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.

Answer: 2

 Nov 9, 2023

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