A club with 13 members is to choose three officers: president, vice-president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled

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saabrrinnaaa

03.08.2020

Mathematics

Part A: Geometric Sequence

Part B: $a_1 = 4, a_n = 2a_{n-1}$

Part C: a₈ = 512

Step-by-step explanation:

When we find the common ratio between the y-values (x-values are n inputs), we should see that we get r = 2. That means we have a geometric sequence.

Because we have a geometric sequence, our recursive formula is: $a_1, a_n=ra_{n-1}$ . Simply plug in our known variables:

$a_1 = 4, a_n = 2a_{n-1}$

Now we need to find what y is when x = 8, so (I used explicit formula):

$a_8 = 4(2)^{8-1}$

a_8=4(128)

a₈ = 512

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A club with 13 members is to choose three​ officers: president,​ vice-president, and​ secretary-treasurer. If each office is to be held by one person and no person can hold more than one​ office, in how many ways can those offices be​ filled