What is the 17th term of the arithmetic sequence 15, 19, 23, ...?

1 Answer
Feb 7, 2016

79

Explanation:

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

19-15 =41915=4
23-19=42319=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(n1)

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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(n1) 15+4(171)

=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(i1)