Questions : 1. Find the 17th term of sequence 3, 9, 27, 81, and so on. 2. Which of term of the sequence 7, 15, 23, is 255 ? 3. Find the 35th term of the Fibonacci sequence 1, 1, 2, 3,…
Questions : 1. Find the 17th term of sequence 3, 9, 27, 81, and so on. 2. Which of term of the sequence 7, 15, 23, is 255 ? 3. Find the 35th term of the Fibonacci sequence 1, 1, 2, 3,…
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
Questions :
1. Find the 17th term of sequence 3, 9, 27, 81, and so on.
2. Which of term of the sequence 7, 15, 23, is 255 ?
3. Find the 35th term of the Fibonacci sequence 1, 1, 2, 3,…
4. Find the sum of the sum sequence 4, 8, 12,… 120. 5. Find the sum of the number sequence 3, 6, 12, 24…until 12,288.
Transcribed Image Text:Solution 1:
1+ V5
- V5
2
Fn
V5
%3D
20
20
|1+ V5
- V5
3.236067977
-1.236067977
Fn
2
2
2
V5
E 20
1.618033989
-0.6180339885
Fn
V5
15,126.9999 – 6.610696082 x 10-5
15,126.9999
2.236067977
2.236067977
15,126.9999 - 0.00006610
%3D
Fn= 6,765 final ans.
2.236067977
Solution 2:
50
1+ V5
50
- V5
2
2
Fn
V5
50
–1.236067977
%3D
50
3.236067977
Fn
V5
50
|1.61803398989--0.618033989;
V5
%3D
Fn
%3D
2.814375334x 1010- 3.553186442 x 10-11
28,143,753,340
2.236067977
2.236067977
28,143,753,340 – 0.000000000
Fn=12,586,269,120
2.236067977
B. Arithmetic Sequence
- It is a sequence of numbers in which the fixed number called the
"common difference(d)"is added to any term to get the next term.
Y Finding the Last term(An)
Formula: an = a1 + (n– 1) d
where: an = last term n = number of term
a, = first termd = common difference
1.
Find the 35th of the sequence 1, 4, 7,..
Given :a, = 1
an = a1 + (n - 1)d
= 1 + (35 – 1)(3)
d= 3
n= 35
2. Which term of the sequence 5, 8, 11, 14,.. is 65?
Given :a, = 5
d= 3
An = 65
= 1 + (34)(3)
= 103
an = a1 + (n – 1)d
= 5 + (n-1)(3)
65 = 5 + 3n – 3
5-3 = 2
65-2 = 3n
n = 21
![V Finding the Sum of the term(S)
• Formula:
S„=la, + an )
S,=(2a, (n – 1)d]
Example:
1. Find the sum of the odd numbers from 1 to 99.
Odd numbers are 1, 3, 5, 7, 9,..
Given: a = 1
Un= 99 n=?
S,=1+ 99)
Solution: S=la, + a, }
an = a1 +7n – 1)d
99= 1 + (n - 1) (2)
99 = 1 + 2n – 2
%3D
50
Sn=(1 + 99)
= 25(100)
Sn = 2,500
n = 50
C. Geometric Sequence
- It is a sequence of number in which the fixed number
called the "common ratio" is multiplied to any term to get the
next term.
• Formula :
an = a,rn-1
where: un = last term n= number of term
r= common ratio a, = first term
Example :
1. Find the 12th term of the sequence 2, 8, 32, and so on.
Given: a, = 2 n= 12
7 = 4
an=?
Solution: a, = a1r"-1
an = 2(4)12 1
a, = 2(4, 194, 304)
a, = 2(4)11
a12 = 8,388,608
v The sum of the term of a Geometric
Sequence
a1(r" –1)
Sn=
r-1
• Find the sum of the first eight terms of the sequence 4, 12 , 36,...
• Given: a = 4
n= 8
r= 3
S=?
Sn=
a1(r" –1)
Sn=
2
4(6560)
r -1
4(38 –1)
Sn=
3 -1
Sn= 2(6560)
4(6,561–1)
Sn=
1
2
Sn=13,120](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11cf9948-466f-4f83-b1e8-3d3186a919f8%2Ff5dd4e40-b906-4cb9-9f03-352218049275%2Fuhownc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:V Finding the Sum of the term(S)
• Formula:
S„=la, + an )
S,=(2a, (n – 1)d]
Example:
1. Find the sum of the odd numbers from 1 to 99.
Odd numbers are 1, 3, 5, 7, 9,..
Given: a = 1
Un= 99 n=?
S,=1+ 99)
Solution: S=la, + a, }
an = a1 +7n – 1)d
99= 1 + (n - 1) (2)
99 = 1 + 2n – 2
%3D
50
Sn=(1 + 99)
= 25(100)
Sn = 2,500
n = 50
C. Geometric Sequence
- It is a sequence of number in which the fixed number
called the "common ratio" is multiplied to any term to get the
next term.
• Formula :
an = a,rn-1
where: un = last term n= number of term
r= common ratio a, = first term
Example :
1. Find the 12th term of the sequence 2, 8, 32, and so on.
Given: a, = 2 n= 12
7 = 4
an=?
Solution: a, = a1r"-1
an = 2(4)12 1
a, = 2(4, 194, 304)
a, = 2(4)11
a12 = 8,388,608
v The sum of the term of a Geometric
Sequence
a1(r" –1)
Sn=
r-1
• Find the sum of the first eight terms of the sequence 4, 12 , 36,...
• Given: a = 4
n= 8
r= 3
S=?
Sn=
a1(r" –1)
Sn=
2
4(6560)
r -1
4(38 –1)
Sn=
3 -1
Sn= 2(6560)
4(6,561–1)
Sn=
1
2
Sn=13,120
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning