Question

The first and last terms of an AP are a and I respectively. Show that the
sum of the nth term from the beginning and the nth term from the end is (a + 1).

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Answer 1

Answer:

Hope it helps you

Step-by-step explanation:

Given: The First term of the AP = a

Given : The Last term of the AP = l.

Given : Total number of terms = n.

Common difference from the beginning = d.

Common difference from the end = -d.

∴ The last term of the AP = nth term of the AP

⇒ an = l

⇒ a + (n - 1) x d = l

 Now,

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

⇒ nth term from the end = l + (n - 1) x (-d)

                                         = l - (n - 1) x d

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

⇒ a + (n - 1) x d + [l - (n - 1) x d]

⇒ a + (n - 1) x d + l - (n - 1) x d

⇒ a + nd - d + l - nd + d

⇒ a + l.