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natta225 [31]
3 years ago
10

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for t

he first term. 50, 100, 150, 200, .
Mathematics
1 answer:
Leokris [45]3 years ago
4 0

Answer:

50n

Step-by-step explanation:

This problem can be solved using concept of Arithmetic progression(AP)

In AP series

the series increases or decreases by certain number which is called common difference.

common difference d is given by

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

nth term = a + (n-1)d

where a is the first term of the series

thus series can be a , a+d, a+2d, a+3d, a+4d, ...........a + (n-1)d

_______________________________________

Given series

50, 100, 150, 200

a = 50

to find d lets use 3rd term as nth term and 2nd term as (n-1)th term

d = 150 -100 = 50

Thus,

nth term = 50 + 50(n-1) = 50 + 50n -50 = 50n

50n can represent the position of the term of the sequence.

To validate this lets put n = 4

50*4 = 200 which is the same as the fourth term given in the series.

hence our solution is correct.

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aleksley [76]

There are 122,100 public school teachers in Ohio and Ohio has a population of 11.6 million people. Illinois has a population of 12.9 million people. If the number of public school teachers per capita in Illinois was proportional to that of Ohio, how many public school teachers would we expect Illinois to have?

This problem uses proportionality or the relationship between two values. Typically, proportions are expressed as fractions. So, we can set this up as

\frac{Teachers}{Population} and we can use this to express both of our values. So, for Ohio, we have \frac{122,100}{11,600,000} and for Illinois we have \frac{x}{12,900,900}. Now, because they are proportional, we can set them equal to each other and we get \frac{122,100}{11,600,00} = \frac{x}{12,900,000}. Now we can cross multiply to get $11,600,000x=1446090000000$ . To get the $x$ alone on one side, we divide by$11,600,000$ and we get 124,662.931034, which is about equal to 124,663.

Therefore, we expect Illinois to have 124,663 public school teachers

4 0
3 years ago
Type the numerical answer ONLY. (no spaces)
Fantom [35]

Answer:

98

Step-by-step explanation:

Mathematically, when we add all the angles of a triangle, we get 180

Thus;

x + 1 + 2x-2+ 3x-5 = 180

6x-6 = 180

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x = 186/6

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so the measure of the biggest angle is 3x -5

= 3(31) + 5 = 93 + 5 = 98

7 0
3 years ago
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