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

Feb 7, 2016

79

#### Explanation:

$\textcolor{b l u e}{\text{Investigation the relationships}}$

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

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$\textcolor{b l u e}{\text{Building the equation}}$

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

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

and3^("rd")" term is "15+8

So the ${n}^{\text{th}}$ term is: $15 + 4 \left(n - 1\right)$

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$\textcolor{b l u e}{\text{Determining the "17^("th")" term}}$

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

$= 15 + 64 = 79$

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$\textcolor{b r o w n}{\text{Introduction to a mathematical way of presenting a sequence}}$

Let a term be represented with the letter $a$

So term 1 would be$\text{ } {a}_{1}$

and term 1 would be$\text{ } {a}_{2}$

and the ${n}^{\text{th}}$ term would be $\text{ } {a}_{n}$

What you would sometimes see is:

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

$\textcolor{g r e e n}{\text{So your sequence could be } {a}_{i} = {a}_{1} + 4 \left(i - 1\right)}$