Mathematics
For an A.P., show that :
(m + n)th term + (m - n)th term = 2 × mth term.
AP
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Answer
L.H.S. = am + n + am - n
= a + (m + n - 1)d + a + (m - n - 1)d
= a + md + nd - d + a + md - nd - d
= 2a + 2md - 2d
= 2(a + md - d)
= 2[a + (m - 1)d]
= 2am = R.H.S.
Hence, proved that (m + n)th term + (m - n)th term = 2 × mth term.
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