If
are in AP, prove that x, y, z are in AO
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Given that
We know, if each term is increased by any real number k, the resultant number are in AP
On adding 1 in each term, we get
On dividing each term by x + y + z, we get
We know, 3 number a, b, c are in AP, iff b - a = c - b
So,
Hence, Proved
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ADDITIONAL INFORMATION
if each term is decreased by any real number k, the resultant number are in AP
if each term is multiplied by any real number k, the resultant number are in AP
if each term is divided by any real number k, the resultant number are in AP
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