Chapter 8.1, Problem 148E

(a)

To determine

To write: the first six terms of the sequence.

Answer to Problem 148E

The first six terms are given by 1, 2, 3, 4, 5, and 6.

Explanation of Solution

Given information:

The graph represents the first six terms of a sequence.

  

Calculation:

From the above graph the first six terms of a sequence are nothing but the second

Coordinates of the points taken in order as shown below

$\left(n,a_n\right)$	$n$	$a_n=n$	Terms
$\left(1,1\right)$	1	$a_1=1$	1st term
$\left(2,2\right)$	2	$a_2=2$	2nd term
$\left(3,3\right)$	3	$a_3=3$	3rd term
$\left(4,4\right)$	4	$a_4=4$	4th term
$\left(5,5\right)$	5	$a_5=5$	5th term
$\left(6,6\right)$	6	$a_6=6$	6th term

Thus, the first six terms are given by 1, 2, 3, 4, 5, and 6.

(b)

To determine

To write: an expression for the apparent $n$ th term $a_n$ of the sequence.

Answer to Problem 148E

The expression for the apparent $n$ th term $a_n$ is given by

  $a_n=n$

Explanation of Solution

Given information:

The graph represents the first six terms of a sequence.

  

Calculation:

Here,

  $\begin{array}{l}n:1234\mathrm{...}n\\ \text{Terms}:123\mathrm{4...}{a}_n\end{array}$

The expression for the apparent $n$ th term $a_n$ is given by

  $a_n=n$

(c)

To determine

To represent: the partial sum of the first 50 terms of the sequence.

Answer to Problem 148E

The sigma notation to represent the partial sum of the first 50 terms of the sequence is given by $S_{50}={\displaystyle \sum _{i=1}^{50}{a}_i}$ .

Explanation of Solution

Given information:

The graph represents the first six terms of a sequence.

  

Calculation:

The $n$ th partial sum is given by

  $S_n=a_1+a_2+a_3+a_4+\mathrm{...}+a_n$

Now represent the above partial sum by using sigma notation as

  $S_n={\displaystyle \sum _{i=1}^n{a}_i}$

Replace, $n=50$

Then,

  $S_{50}={\displaystyle \sum _{i=1}^{50}{a}_i}$

Thus, the sigma notation to represent the partial sum of the first 50 terms of the sequence is given by $S_{50}={\displaystyle \sum _{i=1}^{50}{a}_i}$ .