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Deepak Bora
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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 (a+l)

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ICSE & CBSE Board Question Based on Arithmetic Progression of RS Aggarwal
Here the First and last term of an AP is given. You have to show that the sum of AP from the beginning and ending nth term is (a+l)
This is the Question Number 28 Of Exercise 11 A of RS Aggarwal Solution.

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  1. 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

     

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