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

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

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Answer 1 · 2016-02-07T19:48:09

79

Explanation:

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

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

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

So $1^{st} term is 15 + 0$ $1^("st")" term is "15+0$

and $2^{nd} term is 15 + 4$ $2^("nd")" term is "15+4$

and $3^{rd} term is 15 + 8$ $3^("rd")" term is "15+8$

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

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

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

$= 15 + 64 = 79$ $=15+64=79$

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

Let a term be represented with the letter $a$ $a$

So term 1 would be $a_{1}$ $" "a_1$

and term 1 would be $a_{2}$ $" "a_2$

and the $n^{th}$ $n^("th")$ term would be $a_{n}$ $" "a_n$

What you would sometimes see is:

$Let a_{i} be any term from a_{1} to a_{n}$ $color(brown)("Let "a_i" be any term from "a_1 " to "a_n$

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

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

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