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. Solution 1:1+ V5- V52FnV5%3D2020|1+ V5- V53.236067977-1.236067977Fn222V5E 201.618033989-0.6180339885FnV515,126.9999 – 6.610696082 x 10-515,126.99992.2360679772.23606797715,126.9999 - 0.00006610%3DFn= 6,765 final ans.2.236067977Solution 2:501+ V550- V522FnV550–1.236067977%3D503.236067977FnV550|1.61803398989--0.618033989;V5%3DFn%3D2.814375334x 1010- 3.553186442 x 10-1128,143,753,3402.2360679772.23606797728,143,753,340 – 0.000000000Fn=12,586,269,1202.236067977B. 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) dwhere: an = last term n = number of terma, = first termd = common difference1.Find the 35th of the sequence 1, 4, 7,..Given :a, = 1an = a1 + (n - 1)d= 1 + (35 – 1)(3)d= 3n= 352. Which term of the sequence 5, 8, 11, 14,.. is 65?Given :a, = 5d= 3An = 65= 1 + (34)(3)= 103an = a1 + (n – 1)d= 5 + (n-1)(3)65 = 5 + 3n – 35-3 = 265-2 = 3nn = 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 = 1Un= 99 n=?S,=1+ 99)Solution: S=la, + a, }an = a1 +7n – 1)d99= 1 + (n - 1) (2)99 = 1 + 2n – 2%3D50Sn=(1 + 99)= 25(100)Sn = 2,500n = 50C. Geometric Sequence- It is a sequence of number in which the fixed numbercalled the "common ratio" is multiplied to any term to get thenext term.• Formula :an = a,rn-1where: un = last term n= number of termr= common ratio a, = first termExample :1. Find the 12th term of the sequence 2, 8, 32, and so on.Given: a, = 2 n= 127 = 4an=?Solution: a, = a1r"-1an = 2(4)12 1a, = 2(4, 194, 304)a, = 2(4)11a12 = 8,388,608v The sum of the term of a GeometricSequencea1(r" –1)Sn=r-1• Find the sum of the first eight terms of the sequence 4, 12 , 36,...• Given: a = 4n= 8r= 3S=?Sn=a1(r" –1)Sn=24(6560)r -14(38 –1)Sn=3 -1Sn= 2(6560)4(6,561–1)Sn=12Sn=13,120

(1) The given sequence is 3,9,27,81,... The main objective is to find the 17th term of the given…

Answered: Questions : 1. Find the 17th term of…

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...

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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.

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

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4. Show Solution
13.