If a 1 , … , a 9 are in H.P., a 4 = 5 and a 5 = 4 , find the determinant: a 1 a 4 a 7 a 2 a 5 a 8 a 3 a 6 a 9 .

Question

If a 1 ​ , … , a 9 ​ are in H.P., a 4 ​ = 5 and a 5 ​ = 4 , find the determinant: ​ a 1 ​ a 4 ​ a 7 ​ ​ a 2 ​ a 5 ​ a 8 ​ ​ a 3 ​ a 6 ​ a 9 ​ ​ ​ .

TestHub · Accepted Answer

The reciprocals form an A.P. Since 1/ a 4 ​ = 1/5 and 1/ a 5 ​ = 1/4 , its common difference is 1/20 and its first term is 1/20 . Hence a i ​ = 20/ i . Therefore the determinant equals 2 0 3 ​ 1 1/4 1/7 ​ 1/2 1/5 1/8 ​ 1/3 1/6 1/9 ​ ​ = 21 50 ​ , option C.

Mathematics - Sequence & Series Question with Solution | TestHub

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