Name the constant differences of the sequence 20, 21, 26, 35, 48...
What does "constant differences" mean?
Thank you so much! :)
suppose you subtract the second - first = 1
third - second = 5
fourth - third = 9
fifth - fourth = 13
to get the "first differences" of 1,5,9,13
now suppose we repeat the same procedure
5-1 = 4
9-5 = 4
13-9 = 4
notice we now have "constant differences" but we had to do it twice.
general concept:
if the first differences are constant, then the data came from a first degree relation
if the second differences are constant, then the data came from a second degree, or quadratic relation
if the third ....
This site may help.
http://www.icoachmath.com/SiteMap/ConstantFunction.html
"Constant differences" refers to the difference between consecutive terms in a sequence. In other words, it is the amount by which each term is increasing or decreasing relative to the previous term.
To find the constant differences of a sequence, you simply subtract each term from its consecutive term. In this case, we can find the constant differences as follows:
Difference between 21 and 20: 21 - 20 = 1
Difference between 26 and 21: 26 - 21 = 5
Difference between 35 and 26: 35 - 26 = 9
Difference between 48 and 35: 48 - 35 = 13
Therefore, the constant differences of the given sequence are 1, 5, 9, and 13.