There are four numbers of which the first three are in G.P. and the last three are in A.P., whose common difference is 6 . If the first and the last numbers are equal then two other numbers are

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Let the last three numbers in A.P. be a, a +6 , a + 12 , then the first term is alsoa +12 . But a + 12 , a , a + 6 are in G.P. ∴ a 2 = ( a + 12 ) ( a + 6 ) ⇒ a 2 = a 2 + 18 a + 72 ∴ a = − 4 ∴ The numbers are 8,-4,2,8.

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