5,12,8,6,2,10,7 find the measure of central tendency

Median = 7; Mode = None; Mean = 7.14

Step-by-step explanation:

Measures of Central Tendency represent the distribution of a set of numbers or data.  Median represents the middle number when ordered from least to greatest, Mode represents the most occuring number and Mean represents the average.  In this case, the first step is to number the data set in order from least to greatest (2, 5, 6, 7, 8, 10, 12).  Then you find the middle number in the set of data, which in this case is 7.  Next, you look for the most occuring number, but since all numbers in this data set occur only once each, there is no Mode.  Mean is the average, or the sum of all the numbers divided by the total numbers in the data set (50/7), or 7.14.  

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: