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Writing and Using Explicit Rules for Arithmetic Sequences

Writing and Using Explicit Rules for Arithmetic Sequences 1.3 - Solution

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To find certain terms in a sequence described by an explicit formula, substitute the number of the desired term into the formula to get the term's value. For the given explicit formula, an=5+(n1)(-3),\begin{gathered} a_n=5+(n-1)(\text{-}3), \end{gathered} we can find the second,{\color{#0000FF}{\text{second}}}, fourth,{\color{#009600}{\text{fourth}}}, and eleventh{\color{#FF0000}{\text{eleventh}}} terms of the sequence by substituting 2,{\color{#0000FF}{2}}, 4,{\color{#009600}{4}}, and 11{\color{#FF0000}{11}} into the formula for n.n.
an=5+(n1)(-3)a_n=5+(n-1)(\text{-}3)
a2=5+(21)(-3)a_{{\color{#0000FF}{2}}}=5+({\color{#0000FF}{2}}-1)(\text{-}3)
a2=5+(1)(-3)a_{2}=5+(1) (\text{-}3)
a2=5+(-3)a_{2}=5+(\text{-}3)
a2=53a_{2}=5-3
a2=2a_{2}=2
Now, let's do the same thing for the fourth{\color{#009600}{\text{fourth}}} and eleventh{\color{#FF0000}{\text{eleventh}}} terms.
nthn^{\text{th}} term 5+(n1)(-3)5+(n-1)(\text{-} 3) ana_n
2{\color{#0000FF}{2}} 5+(21)(-3)5+({\color{#0000FF}{2}}-1)(\text{-} 3) 22
4{\color{#009600}{4}} 5+(41)(-3)5+({\color{#009600}{4}}-1)(\text{-} 3) -4\text{-} 4
11{\color{#FF0000}{11}} 5+(111)(-3)5+({\color{#FF0000}{11}}-1)(\text{-} 3) -25\text{-} 25

The second, fourth, and eleventh terms are 2,2, -4,\text{-} 4, and -25.\text{-} 25.