color(blue)("Investigation the relationships")Investigation the relationships
19-15 =419−15=4
23-19=423−19=4
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color(blue)("Building the equation")Building the equation
So 1^("st")" term is "15+01st term is 15+0
and 2^("nd")" term is "15+42nd term is 15+4
and3^("rd")" term is "15+83rd term is 15+8
So the n^("th")nth term is: 15+4(n-1)15+4(n−1)
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color(blue)("Determining the "17^("th")" term")Determining the 17th term
Thus the 17^("th")17th term is 15+4(n-1)" "->" "15+4(17-1)15+4(n−1) → 15+4(17−1)
=15+64=79=15+64=79
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color(brown)("Introduction to a mathematical way of presenting a sequence")Introduction to a mathematical way of presenting a sequence
Let a term be represented with the letter aa
So term 1 would be" "a_1 a1
and term 1 would be" "a_2 a2
and the n^("th")nth term would be " "a_n an
What you would sometimes see is:
color(brown)("Let "a_i" be any term from "a_1 " to "a_nLet ai be any term from a1 to an
color(green)("So your sequence could be " a_i=a_1+4(i-1))So your sequence could be ai=a1+4(i−1)