Determina si 2018 es un termino de la siguiente progresion aritmetica 17,46,75,104,133,....
1 answer:
2018 is the 70th term of the progression.
Explanation
We start out finding the common difference of the progression:
46-17 = 29
Now we write the explicit formula for the sequence. It is of the form
We set this equal to 2018 to see if the answer is a whole number. If it is, it will be the term number that gives us 2018:
2018=17+29(n-1)
Using the distributive property,
2018=17+29*n-29*1
2018=17+29n-29
Combine like terms:
2018=29n-12
Add 12 to both sides:
2018+12=29n-12+12
2030=29n
Divide both sides by 29:
2030/29=29n/29
70=n
Since n=70, this means 2018 is the 70th term of the sequence.
Explanation
We start out finding the common difference of the progression:
46-17 = 29
Now we write the explicit formula for the sequence. It is of the form
We set this equal to 2018 to see if the answer is a whole number. If it is, it will be the term number that gives us 2018:
2018=17+29(n-1)
Using the distributive property,
2018=17+29*n-29*1
2018=17+29n-29
Combine like terms:
2018=29n-12
Add 12 to both sides:
2018+12=29n-12+12
2030=29n
Divide both sides by 29:
2030/29=29n/29
70=n
Since n=70, this means 2018 is the 70th term of the sequence.
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<h2>The stone fall in air for 7 seconds and fall in water for 5 seconds.</h2>
Step-by-step explanation:
Total distance to sea bed = 127 m
Let the distance traveled in air be s.
Distance traveled in water = 127 - s
Average velocity in air = 16 m/s
Average velocity in water = 3 m/s
Distance traveled in air = Average velocity in air x Time in air
s = 16 x t₁
Distance traveled in water = Average velocity in water x Time in water
127-s = 3 x t₂
We have total time is 12 seconds
That is
t₁ + t₂ = 12
We have
s = 16 x t₁
112 = 16 x t₁
t₁ = 7 s
t₁ + t₂ = 12
7 + t₂ = 12
t₂ = 5 s
The stone fall in air for 7 seconds and fall in water for 5 seconds.