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Alekssandra [29.7K]
3 years ago
12

A pool pass costs $30 for the first month and $15 each additional month. Construct an explicit rule in function notation to mode

l the arithmetic sequence. F(n) = ___________ (simplfy your answer) Find F(12)
Mathematics
1 answer:
noname [10]3 years ago
4 0

Answer:

F(n)=15(n+1)    [ where n is number of months]

F(12)=195

Step-by-step explanation:

Pool pass cost for first month =$30

Pool pass cost after first month = $15 for each month

The total amount charged by the pool can be expressed as a  function F(n) where n represents the number of months.

F(n)=15(n-1)+30

This can be simplified by using distribution.

F(n)=(15n-15)+30

F(n)=15n-15+30

F(n)=15n+15

Take 15 as greatest common factor.

∴ F(n)=15(n+1)

For n=12

F(12)=15(12+1)

F(12)=15(13)

F(12)=195

∴ Amount charged by pool for 12 months = $195

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lisov135 [29]

Answer:

4th term = 28

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6th term = 45

Step-by-step explanation:

f(n + 1) = f(n) + 8

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In arithmetic series

Nth term is given by

n th term = a + (n-1)d

where a is the first term

and d is the common difference.

common difference d = nth term - (n-1)th term

For this series

a = 5

lets take nth term as 2nd term and 1st term as (n-1)th term

d = 13-5 = 8

n th term = a + (n-1)d

using the formula for nth term

4th term = 5 + (4-1)8 = 29

5th term = 5 + (5-1) 8= 37

6th term = 5+ (6-1)8 = 45

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5th term =  37

6th term = 45

Note this, problem can be solved using f(n + 1) = f(n) + 8 by putting n = 3,4,5 as well but for learning concept of arithmetic series, i have used above process. Hope it helps.

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an astronaut drops a rock into a crater on the moon. the distance, d(t), in meters, the rock travels after t seconds can be mode
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