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

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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.

  Is there an error in this question or solution?
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RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Exercise 19.2 | Q 22 | Page 12
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