Question

The first and the last term of an a.p are a and l respectively. Show that the sum of the nth term from the beginning and the nth term from the end is (a+l)​

Answer 1

Answer:

sn=n/2 (2a+(n-1)d

Step-by-step explanation:

sn=n/2(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.