Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# The First and the Last Terms of an A.P. Are a and L Respectively. Show that the Sum of Nth Term from the Beginning and Nth Term from the End is a + L. - Mathematics

The first and the last terms of an A.P. are a and l respectively. Show that the sum of nthterm from the beginning and nth term from the end is a + l.

#### Solution

Given:
First term =a
Last term = l
nth term from the beginning  = $a + (n - 1)d$

where d is the common difference.
nth term from the end = $l + (n - 1)( - d) = l - dn + d$

Their sum = $a + (n - 1)d + l - dn + d$

$= a + nd - d + l - nd + d$

$= a + l$

Hence, proved.

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Exercise 19.2 | Q 22 | Page 12