Question

the first and last term of an AP are a and l respectively. show that the sum of the nth term from the beginning and the nth term from the end is

Answer 1

l=a+(n-1)d
a,a+d,a+2d...............l
from last
l,l-d................a
nth term  from beggining
An=a+(n-1)d
from  ending
An=l+(n-1)(-d)

Answer 2

Answer:

Given: First term of the AP = a

Given : Last term of the AP = 1.

Given : Total number of terms = n.

Common difference from the beginning=d

Common difference from the end = -d.

.. Last term of the AP = nth term of the AP

» an = |

» a + (n - 1) * d = 1

Now,

→nth term of the AP from the beginning an = a + (n - 1) * d

→ nth term from the end = 1 + (n - 1) * (-d)

= 1 - (n - 1) * d

Sum of nth term from the beginning + nth term from the end is given by:

→a + (n - 1) * d + [1 - (n - 1) * d]

→ a + (n - 1) * d+1- (n - 1) * d

→ a + nd - d +1- nd + d

→a + 1.