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3 years ago

Select the expression in terms of n

Mathematics

1 answer:

Bumek [7]3 years ago

6 0

Answer:

2n - 11

Step-by-step explanation:

Note there is a common difference d between consecutive terms of the sequence, that is

d = - 7 - (- 9) = - 5 - (- 7) = - 7 + 9 = - 5 + 7 = 2

This indicates the sequence is arithmetic with n th term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 9 and d = 2, thus

$a_{n}$ = - 9 + 2(n - 1) = - 9 + 2n - 2 = 2n - 11

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Answer:

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Step-by-step explanation:

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To make this easier to deal with, we can plug in 8 first:

$\frac{f(8)}{g(8)}=\frac{3-2(8)}{\frac{1}{(8)}+5 }$
Then we can simplify the terms to get $\frac{3-16}{\frac{1}{8} +5}=\frac{-13}{\frac{1}{8} +5}$
The denominator of this fraction needs to have its own common denominator. To do so, we can multiply the 5 by $\frac{8}{8}$ to give us: $\frac{1}{8}+\frac{40}{8}$
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Now putting this back into our original fraction we have: $\frac{-13}{\frac{41}{8} }$
This is also equivalent to $\frac{(\frac{-13}{1} )}{(\frac{41}{8} )}$ which means we need to take the whole denominator of the fraction and flip it and multiply it by the numerator to get: $\frac{-13}{1}*\frac{8}{41}$
This then simplifies to $\frac{-104}{41}$

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