Introduction of Algebra:
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. I like to share this free online algebra 2 help with you all through my article.
(Source Wikipedia).
Algebraic expression for practice:
Constant in algebraic expression :
A symbol in algebra which as fixed value, i.e. ,whose value does not change is called a constant.
For example:
8,-7,0,6*7/8 etc. are all constants.
Variable in algebraic expression:
The different numerical values are assumed by a symbol, is called a variable. In algebraic expression the constant are represented by the 1st world in English alphabet, viz ; a, b, c,………and the variable by the last letters, viz x ,y, z.
The mth term:
The mth term, Dn of the arithmetic progression is;
Dn = c+(m-1)b
The sum of the first m, term
The total of the 1st m object of the arithmetic algebraic progression is :
Rn =m/2 [2c+(m-1)b]
Geometric progression :
Consider the following geometric ;progression :
C+cq+cq2+cq3+……
Where
C is the scale factor.
Q is the common ratio.
The mth term :
The mth term, Dn of the geometric progression is:
Dn = cqm-1.
The sum of the first m terms,
The sum of the first m terms, Dn is :
Rn = c(1-qm)/1-q .
The sum to identify:
If -1< q< 1, the sum to infinity, R is :
R = c/1-q
Having problem with Algebra Math Problems keep reading my upcoming posts, i will try to help you.
Algebraic Expressions Practice problems:
Algebraic expression practice problem1:
The algebraic geometrical progression 1st object of geometrical progression is three, and the ratio two; To determine the term and the sum of the series.
Solution:
We have given
C= 3; q = 2; m = 12;
When by formula,
K = c*qm-1
K = 3*211 = 3* 2048 = 6144
R = c(qm-1) / (q-1)
R = 3(212-1) / (2-1) = 3*4095 = 12285
Algebraic expression practice problem 2:
1820 is the value of the geometrical progression. The series of numbers six, and the ratio three; find the first term, and the last term.
Solution:
We have given
R = 1820, m = 6, q = 3;
By formula,
R= c(qm-1) / (q-1)
1820 = c(36-1) / (3-1) = 364c ;
C = 5, First term.\
Then by formula,
K = c*qm-1
K = 5*35 =1215, Last term
The first term is; c = 5
The last term is: k= 1215
Algebraic expression practice problem 3:
To determine the three algebraic geometrical expression means between 6 and 486.
Solution;
By formula. We have
S = `root(4)(486/6)` = `root(4)(81)` =3
Therefore the series 6,18,54, 162,486. ( 6 * 3 = 18 , 18 * 3 = 54 , 54 * 3 = 162)
Answer is 6, 18, 54, 162,486.
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. I like to share this free online algebra 2 help with you all through my article.
(Source Wikipedia).
Algebraic expression for practice:
Constant in algebraic expression :
A symbol in algebra which as fixed value, i.e. ,whose value does not change is called a constant.
For example:
8,-7,0,6*7/8 etc. are all constants.
Variable in algebraic expression:
The different numerical values are assumed by a symbol, is called a variable. In algebraic expression the constant are represented by the 1st world in English alphabet, viz ; a, b, c,………and the variable by the last letters, viz x ,y, z.
The mth term:
The mth term, Dn of the arithmetic progression is;
Dn = c+(m-1)b
The sum of the first m, term
The total of the 1st m object of the arithmetic algebraic progression is :
Rn =m/2 [2c+(m-1)b]
Geometric progression :
Consider the following geometric ;progression :
C+cq+cq2+cq3+……
Where
C is the scale factor.
Q is the common ratio.
The mth term :
The mth term, Dn of the geometric progression is:
Dn = cqm-1.
The sum of the first m terms,
The sum of the first m terms, Dn is :
Rn = c(1-qm)/1-q .
The sum to identify:
If -1< q< 1, the sum to infinity, R is :
R = c/1-q
Having problem with Algebra Math Problems keep reading my upcoming posts, i will try to help you.
Algebraic Expressions Practice problems:
Algebraic expression practice problem1:
The algebraic geometrical progression 1st object of geometrical progression is three, and the ratio two; To determine the term and the sum of the series.
Solution:
We have given
C= 3; q = 2; m = 12;
When by formula,
K = c*qm-1
K = 3*211 = 3* 2048 = 6144
R = c(qm-1) / (q-1)
R = 3(212-1) / (2-1) = 3*4095 = 12285
Algebraic expression practice problem 2:
1820 is the value of the geometrical progression. The series of numbers six, and the ratio three; find the first term, and the last term.
Solution:
We have given
R = 1820, m = 6, q = 3;
By formula,
R= c(qm-1) / (q-1)
1820 = c(36-1) / (3-1) = 364c ;
C = 5, First term.\
Then by formula,
K = c*qm-1
K = 5*35 =1215, Last term
The first term is; c = 5
The last term is: k= 1215
Algebraic expression practice problem 3:
To determine the three algebraic geometrical expression means between 6 and 486.
Solution;
By formula. We have
S = `root(4)(486/6)` = `root(4)(81)` =3
Therefore the series 6,18,54, 162,486. ( 6 * 3 = 18 , 18 * 3 = 54 , 54 * 3 = 162)
Answer is 6, 18, 54, 162,486.
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