The sum of 3rd and 5th term of an ap is 16 and their product is 60.find the terms of the ap?
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which term nth or 1st 2nd
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Let A be the first term and D be the common difference of AP.
Given, T3 + T5 = 16 ----(1) and T3 × T5 = 60 ---(2)
(1) means, (A+2D) + (A+4D) = 16
A + 3D = 8-----(3)
(2) means, (A+2D) × (A+4D) = 60
Substituting A from (3),
(8-D) × (8+D) = 60
64 - D^2 = 60
D = 2 or -2.
From (3),
If D = 2, A = 2
If D = -2, A = 14.
Therefore AP is:
2, 4, 6, 8, 10,.....
or
14, 12, 10, 8, 6,.....
Given, T3 + T5 = 16 ----(1) and T3 × T5 = 60 ---(2)
(1) means, (A+2D) + (A+4D) = 16
A + 3D = 8-----(3)
(2) means, (A+2D) × (A+4D) = 60
Substituting A from (3),
(8-D) × (8+D) = 60
64 - D^2 = 60
D = 2 or -2.
From (3),
If D = 2, A = 2
If D = -2, A = 14.
Therefore AP is:
2, 4, 6, 8, 10,.....
or
14, 12, 10, 8, 6,.....
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