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

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Answer 1 · 2016-02-07T19:48:09

79

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

$19-15 =4$
$23-19=4$

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

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: $15+4(n-1)$

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

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

$=15+64=79$

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

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:

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

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