Question

The first and last term an ap are a and I respectively show that the sum of the nth term form beginning and the nth from the end is (a +1)

Answer 1

presuming there are n terms and nth term from start is

l=1+(n-1)d

nth term from end would be a so sum is a+l

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