Chapter 12: Q 12.51 (page 1191)

Find the sum.
${\sum 6}_{i = 1}^{15} {(2)}^{i}$

Short Answer

Expert verified

Sum is equal to $\begin{array}{rcl} 393204 \end{array}$

Step by step solution

Step 1. Find the first term and the common ratio.

Consider the sequence ${\sum 6}_{i = 1}^{15} {(2)}^{i}$

Let role="math" localid="1645297852087" $a_{1}, r$ denote the first term and the common ratio respectively.

$\begin{array}{rcl} a_{1} & = & 6 {(2)}^{1} \\ = & 12 \\ a_{2} & = & 6 {(2)}^{2} \\ = & 24 \end{array}$ So,

$\begin{array}{rcl} r & = & \frac{24}{12} \\ = & 2 \end{array}$

Step 2. Find the sum.

Consider the sequence $\sum_{i = 1}^{15} 6 {(2)}^{i}$ .

Sum of the first $n$ terms is given by $S_{n} = \frac{a_{1} (1 - r^{n})}{1 - r}$

So,

$\begin{array}{rcl} \sum_{i = 1}^{15} 6 {(2)}^{i} & = & \frac{12 (1 - 2^{15})}{1 - 2} \\ = & - 12 (1 - 32768) \\ = & 393204 \end{array}$

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Find the sum.
${\sum 6}_{i = 1}^{15} {(2)}^{i}$

Short Answer

Step by step solution

Step 1. Find the first term and the common ratio.

Step 2. Find the sum.

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Find the sum.∑6i=1152i

Short Answer

Step by step solution

Step 1. Find the first term and the common ratio.

Step 2. Find the sum.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Find the sum.
${\sum 6}_{i = 1}^{15} {(2)}^{i}$