Question

The first and last terms 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 ( a + l ).

Answer 1

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qυeѕтιon:

The first and last terms 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 ( a + l ).


ɑղՏաҽɾ:

Given;

First term of the ap , a1 = a

Last term of the ap, al = l

nth term from the beginning of the ap , an = a + (n – 1) d.

nth term from the end of the ap , tn = l – (n – 1) d.

Now, according to the question we get ;

an + tn = [ a + (n – 1) d ] + [ l – (n – 1) d ]

= (a + l)

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Answer 2

Given : First term of the AP = a

Given : Last term of the AP = l.

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 = l

⇒ a + (n - 1) * d = l

Now,

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

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

                                         = l - (n - 1) * d

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

⇒ a + (n - 1) * d + [l - (n - 1) * d]

⇒ a + (n - 1) * d + l - (n - 1) * d

⇒ a + nd - d + l - nd + d

⇒ a + l.

Hope this helps!

Hope this helps!