Chapter 12: Q 12.48 (page 1190)

Find the eleventh term of the sequence $7, 14, 28, 56, 112, 224, \dots$ Then find the general term for the sequence.

Short Answer

Expert verified

The eleventh term of the sequence is $7168$ and the general term is equal to $a_{n} = 7 {(2)}^{n - 1}$

Step by step solution

Step 1. Given information

The sequence is $7, 14, 28, 56, 112, 224, . . .$

Step 2. Find the eleventh term of the sequence.

Consider the sequence:

$7, 14, 28, 56, 112, 256, . . .$

Let $a, r$ denote the first term and the common ratio respectively.

$\begin{array}{rcl} a & = & 7 \\ r & = & \frac{14}{7} \\ = & 2 \end{array}$

$\begin{array}{rcl} a_{n} & = & a r^{n - 1} \\ a_{11} & = & 7 {(2)}^{11 - 1} \\ = & 7 {(2)}^{10} \\ = & 7168 \end{array}$

Step 3. Find the general term of the sequence.

Put $a = 7, r = 2$ in $a_{n} = a r^{n - 1}$ .

$a_{n} = 7 {(2)}^{n - 1}$

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Find the eleventh term of the sequence $7, 14, 28, 56, 112, 224, \dots$ Then find the general term for the sequence.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the eleventh term of the sequence.

Step 3. Find the general term of the sequence.

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Find the eleventh term of the sequence 7,14,28,56,112,224,…Then find the general term for the sequence.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the eleventh term of the sequence.

Step 3. Find the general term of the sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Pure Maths

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find the eleventh term of the sequence $7, 14, 28, 56, 112, 224, \dots$ Then find the general term for the sequence.