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The sum of the three numbers in A.P is 21 and the product of the first and third number of the sequence is 45. What are the three numbers?

A. 5, 7 and 9 B. 9, 7 and 5 C. 3, 7 and 11 D. Both (A) and (B) Answer: Option D
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Solution(By Apex Team)

Let the numbers are be a – d, a, a + d Then a – d + a + a + d = 21 3a = 21 a = 7 and (a – d)(a + d) = 45 $\begin{array}{l} a^{2}-d^{2}=45 \\ d^{2}=4 \\ d=\pm 2 \end{array}$ Hence, the numbers are 5, 7 and 9 when d = 2 and 9, 7 and 5 when d = -2. In both the cases numbers are the same.

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