Arithmetic sequences can be defined as a sequence of a number. It means that sequence of number specify the difference between the consecutive number that is constant. Suppose there is an arithmetic sequence 2, 5, 8, 11, 13, 16…….with the common difference of 3. In mathematics, sometime arithmetic sequence is known as arithmetic progressions. The calculation of arithmetic sequence is very easy to understand. This topic helps to understand basic concepts of grade VII. If the initial number of an arithmetic sequence is ‘x1’ and the difference of the successive members is ‘df’, then the ‘xn’ term of the sequence is given by:
xn = x1 + (n – 1) df,
And in the mathematical terms, it can be defined as,
xn = xm + (n – m) df.
A finite portion of an arithmetic sequence is called as a finite sequence and sometime it is known as arithmetic progression. The total of different arithmetic progression is known as arithmetic series. The number added or subtracted at each stage of an arithmetic sequence is known as the common difference “df”. In simple language, an arithmetic sequence can be defined as a set of number that follows a particular pattern. The term and pattern in the number sequence depends on the behavior of the common difference means on ’df’. Shown below are some of the instances, (know more about ICSE Board Syllabus, here)
a) If the common difference is positive in the sequence then the terms of the sequence grow towards the positive infinity.
b) If the common difference is negative in the sequence then the terms of the sequence grow towards the negative infinity.
The total of arithmetic sequence can be defined as an arithmetic series.
Sequence of ‘n’ numbers = x1 + (x1 + df) + (x1 + 2 * df) + ……… + (x1 + (n – 1) df),
In the next session we will discuss about Multistep problems.
xn = x1 + (n – 1) df,
And in the mathematical terms, it can be defined as,
xn = xm + (n – m) df.
A finite portion of an arithmetic sequence is called as a finite sequence and sometime it is known as arithmetic progression. The total of different arithmetic progression is known as arithmetic series. The number added or subtracted at each stage of an arithmetic sequence is known as the common difference “df”. In simple language, an arithmetic sequence can be defined as a set of number that follows a particular pattern. The term and pattern in the number sequence depends on the behavior of the common difference means on ’df’. Shown below are some of the instances, (know more about ICSE Board Syllabus, here)
a) If the common difference is positive in the sequence then the terms of the sequence grow towards the positive infinity.
b) If the common difference is negative in the sequence then the terms of the sequence grow towards the negative infinity.
The total of arithmetic sequence can be defined as an arithmetic series.
Sequence of ‘n’ numbers = x1 + (x1 + df) + (x1 + 2 * df) + ……… + (x1 + (n – 1) df),
In the next session we will discuss about Multistep problems.
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