Chapter 12: Q 12.46 (page 1189)

Find the twelfth term of a sequence where the first term is $256$ and the common ratio is $r = \frac{1}{4}$ .

Short Answer

Expert verified

The the twelfth term of a sequence is equal to $\frac{1}{4^{7}}$ .

Step by step solution

Step 1. Given information

The first term is $256$ and the common ratio is $r = \frac{1}{4}$ .

Step 2. Find the twelfth term of a sequence.

Let $a$ denotes the first term of the sequence.

$\begin{array}{rcl} a & = & 256 \\ r & = & \frac{1}{4} \\ a_{n} & = & a r^{n - 1} \end{array}$

$\begin{array}{rcl} a_{12} & = & 256 {(\frac{1}{4})}^{12 - 1} \\ = & 4^{4} {(\frac{1}{4})}^{11} \\ = & \frac{1}{4^{7}} \end{array}$

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Find the twelfth term of a sequence where the first term is $256$ and the common ratio is $r = \frac{1}{4}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the twelfth term of a sequence.

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Find the twelfth term of a sequence where the first term is 256 and the common ratio is r=14.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the twelfth term of a sequence.

One App. One Place for Learning.

Most popular questions from this chapter

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Find the twelfth term of a sequence where the first term is $256$ and the common ratio is $r = \frac{1}{4}$ .