What is the value of tan A?
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Consider the lengths of consecutive 1-2 blocks.
block 1 - 1, 2 - length 2
block 2 - 1, 2, 2 - length 3
block 3 - 1, 2, 2, 2 - length 4
block 4 - 1, 2, 2, 2, 2 - length 5
and so on.
Recall the formula for the sum of consecutive positive integers,
Now,
which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.
In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of
numbers, and their sum is
This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of .
So, the sum of the first 1234 terms in the sequence is 2419.
Hello,
First you have order all the number least to the greater. That gives 30, 75, 80, 85, 85, 95, 95, 100, 100, 110.
Afterwards you have to find the median. Why ?
I will explain you. It's because the median is robust. In fact, it can't be influenced by extreme values (example : 110) but the mean yes. So the mean won't be accurate.
"Then why don't you choose the mode ? " you will ask me. That's because the mode takes the number which appears most often in a set of numbers. It couldn't be accurate at all. It will be useless for this set of numbers.
Furthermore, here there are 3 numbers which appears the most ( 2 times for each) : $85, $95 and $100. Which one will you take ?
Therefore the median is the most suitable and the most accurate to know the center because it is robust.
Now, let's find the median :
There are 10 values, so the median will be the average of the 5th and 6th values.
5th value = 85
6th value = 95
Therefore the median is 90.
Hope this helps !
Photon
First you have order all the number least to the greater. That gives 30, 75, 80, 85, 85, 95, 95, 100, 100, 110.
Afterwards you have to find the median. Why ?
I will explain you. It's because the median is robust. In fact, it can't be influenced by extreme values (example : 110) but the mean yes. So the mean won't be accurate.
"Then why don't you choose the mode ? " you will ask me. That's because the mode takes the number which appears most often in a set of numbers. It couldn't be accurate at all. It will be useless for this set of numbers.
Furthermore, here there are 3 numbers which appears the most ( 2 times for each) : $85, $95 and $100. Which one will you take ?
Therefore the median is the most suitable and the most accurate to know the center because it is robust.
Now, let's find the median :
There are 10 values, so the median will be the average of the 5th and 6th values.
5th value = 85
6th value = 95
Therefore the median is 90.
Hope this helps !
Photon