Answer to Question #171119 in Calculus for Angelie Suarez

Question

2. SEQUENCE. 

A. Consider the sequence {Sn} defined by Sn = 2n – 5 where −4 < 𝑛 ≤ 4.

Show complete solution. 

Find for: 

a. 1st element 

b. 5th element 

c. A7 

d. A10 

e. ∏𝑨𝒊

i=3

f. 5

∑𝑨𝒊

i=1

Thinking Box:

The sequence {An} defined by An = 2n – 5 where 𝒏 ≥ 𝟏 is an example of finite or infinite sequence? Why?

Answer 1

CORRECTED SOLUTION

The sequence {Sn} defined by Sn = 2n – 5 where −4 < 𝑛 ≤ 4. Therefore, we have a table

$\begin{matrix} A_1&A_2&A_3&A_4&A_5&A_6&A_7&A_8\\ S_{-3} & S_{-2} & S_{-1} &S_0 &S_1 &S_2 &S_3 &S_4 &\\ -11 & -9 &-7&-5&-3&-1&1&3 \end{matrix}$

a) the 1st element of the sequence is $S_{-3}=-11$

b) the 5th element of the sequence is $S_{1}=-3$

c) the 7th element of the sequence is $S_{3}=1$

d) the 10th element of the sequence doesn't exist

e) $\prod\limits_{i=3}^8 A_i=(-7)\cdot(-5)\cdot(-3)\cdot(-1)\cdot 1\cdot 3=315$

f) $\sum\limits_{i=1}^5 A_i=(-11)+(-9)+(-7)+(-5)+(-3)=-35$

The sequence {An} defined by An = 2n – 5 where 𝒏 ≥ 𝟏 is an example of an infinite sequence, since this sequence is defined for infinitely many indices n.