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Show that the Sum of (M + N)Th And (M – N)Th Terms of an A.P. is Equal to Twice The Mth Term. - Mathematics

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Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.

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Solution

Let a and d be the first term and the common difference of the A.P. respectively.

It is known that the kth term of an A. P. is given by

ak = a + (k –1) d

∴ am + n = a + (m + n –1) d

am – n = a + (m – n –1) d

am a + (m –1) d

∴ am + n + am – n = a + (m + n –1) d + a + (m – n –1) d

= 2a + (m + n –1 + m – n –1) d

= 2a + (2m – 2) d

= 2a + 2 (m – 1) d

=2 [a + (m – 1) d]

= 2am

Thus, the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.

Concept: Arithmetic Progression (A.P.)
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APPEARS IN

NCERT Class 11 Mathematics
Chapter 9 Sequences and Series
Q 1 | Page 199

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