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 DShow Answer
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.
Related Questions On Progressions
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A. 22B. 25
C. 23
D. 24
Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.
A. 5B. 6
C. 4
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Find the 15th term of the sequence 20, 15, 10 . . .
A. -45B. -55
C. -50
D. 0
The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
A. 600B. 765
C. 640
D. 680
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