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Soloha48 [4]
2 years ago
10

Find the first three terms of the arithmetic series described. a_1=1,a_n=19,S_n=100

Mathematics
1 answer:
Rudik [331]2 years ago
3 0

Answer:

1, 3, 5

Step-by-step explanation:

The sum of an arithmetic series is:

S_n = n (a_1 + a_n) / 2

100 = n (1 + 19) / 2

n = 10

The nth term of an arithmetic sequence is:

a_n = a_1 + d (n − 1)

19 = 1 + d (10 − 1)

d = 2

The common difference is 2.  So the first three terms are 1, 3, and 5.

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Josh $600 into an account that pays simple interest at a rate of 4% per year. How much interest will he be paid in the first 4 y
galben [10]

Answer:

i think its 96 dollars

Step-by-step explanation:

600 × .06 = 24

24 × 4 = 96

6 0
3 years ago
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In a geometric sequence, a2=108 and as 256. Write the explicit formula for this sequence.
torisob [31]

Answer:

The first choice is correct.

Step-by-step explanation:

First work out the common ratio r:-

a2 = a1r and a5 = a1 r^4

So r^3 = a1r^4 / a1r = 256/ 108

r = cube root (256/-108) =  4/3

So the explicit formula is 108(4/3)^(n-1)

8 0
3 years ago
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a landscaper is supposed to plant pine trees, oak trees, and elm trees in a ratio of 48:12:120. At this time, the landscaper onl
iogann1982 [59]

Answer:

Step-by-step explanation:

Coniferous trees keep their needles all year with the exception of tamarack. They are good trees to plant for privacy and wind breaks or shelterbelts

Pines include native white, red, and jack. They have long needles.

Spruces, black and white, and firs. They have short needles. They are important sources of wood fiber in northern Minnesota, and are excellent choices for windbreaks or shelterbelts.

Cedars include white or red. Cedars have scaled needles. Smaller than pines and spruces, cedars can provide wildlife cover and food.

5 0
2 years ago
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The number of Apple iPods sold in 2009 was 54.13 million. That number decreased approximately linearly to 26.38 million iPods so
AleksandrR [38]

Answer:

A(t) = -6.9375t + 81.88 is the amount, in millions, for the number of Apple iPods sold in t years after 2005.

Step-by-step explanation:

Linear function:

A linear function has the following function:

y = mx + b

In which m is the slope(the value that y changes by when x changes by 1) and b is the y-intercept(the initial value of the output).

Finding the value in 2005:

This is b.

The number of Apple iPods sold in 2009 was 54.13 million. That number decreased approximately linearly to 26.38 million iPods sold in 2013.

So in 4 years, it decreased from 54.13 - 26.38 = 27.75 million.

So the value in 2005 should also be 27.75 million more than in 2009, that is 54.13 + 27.75 = 81.88. So

y = mx + 81.88

Using A for y and t for x

A(t) = mt + 81.88

Finding the slope:

When we have two points, the slope is given by the change in the output divided by the change in the input.

In 4 years, the amount decrease by 27.75 million. So

m = -\frac{27.75}{4} = -6.9375

So

A(t) = -6.9375t + 81.88 is the amount, in millions, for the number of Apple iPods sold in t years after 2005.

6 0
2 years ago
mr.roxbury weighed 240 pounds when he started on a diet. over a one year period mr.roxbury lost 32% of his body weight. in the f
Annette [7]

Answer:

187.68

Step-by-step explanation:

240*.32=76.8

240-76.8=163.2

163.2*.15=24.48

163.2+24.48=187.68

3 0
2 years ago
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