Use the explicit formula an = a1 + (n – 1) • d to find the 250th term of the sequence below. 57, 66, 75, 84, 93, ...
1 answer:
The general term of an arithmetic sequence is,
Where , = nth term.
= First term
and d = common difference.
The given sequence is: 57, 66, 75, 84, 93, ...
Here = 57,
d = 66 - 57 = 9
We need to find the 250th term. So, n = 250.
Next step is to plug in these values in the above formula. Therefore,
= 57 + 249 * 9
= 57 + 2241
= 2298
Therefore, 250th of this sequence is 2298
Hope this helps you!
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Answer:
19 million
Step-by-step explanation:
So generally whenever we express a exponential function, it's in the form:
where a=initial value aka when x=0
in this case, b can be expressed as: , where r is the growth rate, which in this case is 2.13%, and expressing that as a decimal (divide by 100), r=0.0213, thus b=1.0213
This gives us the following equation:
To kind of give you a intuitive reason as to why this makes sense, think of that 1.0213 wrapping around the previous value.
So when x=0, it's actually just 16, since any number (besides 0) to the power of 0, equals 1.
When x=1, we get: , which can be expressed as a 2.13% increase from year 0
When x=2, we get: , which can be expressed as a 2.13% increase from year 1
when x=3, we get: , which can be expressed as a 2.13% increase from year 2.
In other words, each year we're getting another 1.0213 to multiply by (very definition of an exponent).
So to calculate the population in 1997, we put in x=7, since it's 7 years after 1990
We get the following equation:
Using a calculator this simplifies to approximately:
Rounding this to the nearest integer would yield 19, and since the values are expressed in millions, the answer would be 19 million