#color(blue)("Investigation the relationships")#

#19-15 =4#

#23-19=4#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Building the equation")#

So #1^("st")" term is "15+0#

and #2^("nd")" term is "15+4#

and#3^("rd")" term is "15+8#

So the #n^("th")# term is: #15+4(n-1)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Determining the "17^("th")" term")#

Thus the #17^("th")# term is #15+4(n-1)" "->" "15+4(17-1)#

#=15+64=79#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(brown)("Introduction to a mathematical way of presenting a sequence")#

Let a term be represented with the letter #a#

So term 1 would be#" "a_1#

and term 1 would be#" "a_2#

and the #n^("th")# term would be #" "a_n#

What you would sometimes see is:

#color(brown)("Let "a_i" be any term from "a_1 " to "a_n#

#color(green)("So your sequence could be " a_i=a_1+4(i-1))#