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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 3,9,15, ... Find the 45th term.

User Yeesterbunny
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1 Answer

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20 votes

Given the first three terms of the sequence to be


3,\text{ 9, 15,}\ldots

It is observed that each successive term of the sequence is obtained by the addition of 6 to the preceding term.

Thus, the sequence is an arithmetic sequence.

The nth term of an arithmetic sequence is given as


\begin{gathered} T_n=\text{ a +(n-1)d} \\ \text{where} \\ a\Rightarrow first\text{ term of the sequence} \\ d\Rightarrow common\text{ difference of the sequence, obatined to be the difference betw}een\text{ two consecutive terms of the sequence} \\ n\Rightarrow position\text{ occupied by the term of a sequence} \\ T_n\Rightarrow value\text{ of the nth term of the sequence} \end{gathered}

Thus, from the given sequence,


\begin{gathered} a=3 \\ d=9-3=6\text{ OR 15-9=6} \\ n=45 \\ T_(45)\text{ is thus evaluated as} \\ T_(45)=3\text{ + (45-1)6} \\ T_(45)=3\text{ + (44}*6) \\ T_(45)\text{ = 3 + 264} \\ T_(45)=267 \end{gathered}

The 45th term of the sequence is thus 267

User Hschne
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