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?

1. 5, 7 and 9
2. 9, 7 and 5
3. 3, 7, and 11
4. Both (1) and (2)
5. 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
a² - d² = 45
d² = 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.

Question on finding sum of terms of a GP, Problem on finding a particular term of an AP, given sum of two other terms, Summation of AP having negative common difference, Finding terms of an AP, given sum and product of some of its terms, Sum of series of numbers in arithmetic progression, A CAT 2003 question to find sum of terms of an AP

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