1, 4, 7, 10, ...
The difference between the second and the first term is 4 – 1 = 3. The difference
between the third term and the second term is 7 – 4 = 3.
Also t 2 – t 1 = t 3 – t 2 = t 4 – t 3 = 3.
Since the differences are the same, the difference is called the common difference
and is denoted as ‘d’.
- Common difference
In an Arithmetic progression the difference between any two terms which is same all
through the sequence is called as the common difference and is normally denoted as ‘d’.
- General term
The terms of an A.P are generally denoted as t 1 , t 2 , t 3 , t 4 ,... That is, the first term is t 1 ,
the second term is t 2 etc., and the last term is denoted as tn. The last term of the A.P
is called as the general term and can be found using the formula tn = a +(n-1)d.
Note that if the last term of a sequence is known, then the number of terms in the
sequence denoted as ‘n’ can be found using the formula, n=⎝⎜⎛l−da⎠⎞⎟+^1 , where ‘n’ is
the number of terms in the sequence, ‘l’ is the last term, ‘a’ is the first term and ‘d’
is the common difference.
As this is a simple arithmetic, the child can be taught by presentation of this in
Braille format.
- Increasing sequence
The common difference of an arithmetic progression is normally denoted as ‘d’. If the
value of ‘d’ is positive, then the sequence is an increasing sequence.
Eg. : 1, 4, 7, 10, ...
