Question:
If the sum of the three numbers which are in A.P. is \(27\) and the product of the first and last is \(77\), then the numbers are
If the sum of the three numbers which are in A.P. is \(27\) and the product of the first and last is \(77\), then the numbers are
Show Hint
Three numbers in A.P. are conveniently taken as
\[
\boxed{a-d,\;a,\;a+d.}
\]
Updated On: Jul 18, 2026
- \(6,9,11\)
- \(9,11,14\)
- \(7,9,11\)
- \(9,11,15\)
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The Correct Option is C
Solution and Explanation
Let the numbers be
\[
9-d,\;9,\;9+d
\]
since their sum is
\[
3\times9=27.
\]
Given,
\[
(9-d)(9+d)=77.
\]
So,
\[
81-d^2=77
\]
\[
d^2=4
\]
\[
d=2.
\]
Hence, the numbers are
\[
7,\;9,\;11.
\]
Therefore,
\[
\boxed{(C)}
\]
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