Sequences, Series  CAT 2016 Preparation
Question 4 the day : April 04, 2003
The question for the day is a sample practice problem in sequences, series  progressions. Arithmetic, Geometric and Harmonic progression questions.
Question
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?
 5, 7 and 9
 9, 7 and 5
 3, 7, and 11
 Both (1) and (2)
 None of these
Correct Answer is Both (1) and (2). Correct Choice is (3)
Explanatory Answer
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
a^{2}  d^{2} = 45
d^{2} = 4
d = +2
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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