the first and last term of an AP is a and l.show nth term from begining and nth term from end is a l
nth from front is a + (n-1)d
nth from l is l - (n-1)d
their sum is a+l
Not sure what you meant by "a l"
To find the nth term from the beginning and end of an arithmetic progression (AP) with first term a and last term l, we need to determine the common difference (d) of the AP.
The formula for the nth term in an arithmetic progression is given by:
nth term = a + (n-1)d
Since the first term is a and the nth term from the beginning is given as a, we can substitute these values into the formula:
a = a + (n-1)d
Simplifying this equation, we get:
0 = (n-1)d
This means that the common difference (d) is 0. In an AP with a common difference of 0, all terms are the same. Therefore, the AP is a sequence of a repeated n times.
Similarly, if we consider the nth term from the end, which is also given as l, we substitute these values into the formula:
l = a + (n-1)d
Again, simplifying this equation, we get:
0 = (n-1)d
This means that the common difference (d) is 0. Therefore, all terms of the AP are the same, resulting in a repeated sequence of l.
In conclusion, if the first and last terms of an AP are a and l, respectively, then the nth term from the beginning and end will be a and l, respectively. In such cases, the common difference of the AP is 0, resulting in a repeated sequence of the same term.