I don't get this. Please help
1 answer:
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The number of ways of taking any
and in particular, the total number of ways to picking proper subsets is
Without computing each term directly, let's instead use a direct result from the binomial theorem, which says
If we replace
We can use this to evaluate our sum directly:
Recursive Formula
The top row says the first term is 8
The bottom row says that to get the nth term, we subtract 7 from the (n-1)th term. So basically we subtract 7 from each term to get the next term.
Note the subscripts tell us which term we're working with.
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Arithmetic Formula
We have a = 8 as the first term and d = -7 as the common difference.
a(n) = a + d(n-1)
a(n) = 8 + (-7)(n-1)
a(n) = 8 - 7n + 7
a(n) = -7n+15
The nth term arithmetic formula is a(n) = -7n+15
If you plug in n = 1, you should get a(n) = 8
If you plug in n = 2, you should get a(n) = 1
and so on.
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Finding the 10th term
Plug in n = 10 to get
a(n) = -7n+15
a(10) = -7(10)+15
a(10) = -70+15
a(10) = -55
The 10th term is -55