Chapter 12: Q. 12 (page 1173)

In the following exercise, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{3 n + 3}{3^{n}}$

Short Answer

Expert verified

The first five terms of the sequence whose general term is $a_{n} = \frac{3 n + 3}{3^{n}}$ are $2, 1, \frac{4}{9}, \frac{5}{27}, \frac{2}{27} .$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegeneraltermforthesequenceisgivenas \\ a_{n} = \frac{3 n + 3}{3^{n}} \\ Wehavetofindthefirstfivetermsofthesequence. \end{array}$

Step 2. Calculating the terms

$\begin{array}{l} Wewillsubstitute n = 1, 2, 3, 4 and 5 intheordertoobtainthefirstfivetermsofthesequence. \\ Now, \end{array}$

$\begin{matrix} n : & 1 & 2 & 3 & 4 & 5 \\ a_{n} : & \begin{array}{l} a_{1} = \frac{3 (1) + 3}{3^{1}} \\ = \frac{3 + 3}{3} \\ = \frac{6}{3} \\ = 2 \end{array} & \begin{array}{l} a_{2} = \frac{3 (2) + 3}{3^{2}} \\ = \frac{6 + 3}{9} \\ = \frac{9}{9} \\ = 1 \end{array} & \begin{array}{l} a_{3} = \frac{3 (3) + 3}{3^{3}} \\ = \frac{9 + 3}{27} \\ = \frac{12}{27} \\ = \frac{4}{9} \end{array} & \begin{array}{l} a_{4} = \frac{3 (4) + 3}{3^{4}} \\ = \frac{12 + 3}{81} \\ = \frac{15}{81} \\ = \frac{5}{27} \end{array} & \begin{array}{l} a_{5} = \frac{3 (5) + 3}{3^{5}} \\ = \frac{15 + 3}{243} \\ = \frac{18}{243} \\ = \frac{2}{27} \end{array} \end{matrix}$

Step 3. Conclusion

From the above step, we can conclude that the first five terms of the sequence will be $2, 1, \frac{4}{9}, \frac{5}{27}, \frac{2}{27} .$

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In the following exercise, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{3 n + 3}{3^{n}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the terms

Step 3. Conclusion

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In the following exercise, write the first five terms of the sequence whose general term is given.an=3n+33n

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the terms

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercise, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{3 n + 3}{3^{n}}$