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Three terms in Harmonic Progression. If the third terms decreas by four it is Arithmetic Progression. If the third terms decrease by 3 they are in Geometric Progression. Find the three terms.

Three terms in Harmonic Progression. If the third terms decreas by four it is Arithmetic Progression. If the third terms decrease by 3 they are in Geometric Progression. Find the three terms.

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2 Answers

Ravi
askIITians Faculty 69 Points
8 years ago
Let the HP be 1/a ; 1/b; 1/c
So a,b,c are in AP (i)

If third term of the HP is decreased by 4, i.e. 1/c-4, it makes an AP (ii)
If third term of the HP is decreased by 3, i.e. 1/c-3, it makes an AP (iiI)

for the I, II, III eqns, form 3eqns in 3 variables and solve them to get the answer.
Ravi
askIITians Faculty 69 Points
8 years ago
Let the HP be 1/a ; 1/b; 1/c
So a,b,c are in AP (i)

If third term of the HP is decreased by 4, i.e. 1/c-4, it makes an AP (ii)
If third term of the HP is decreased by 3, i.e. 1/c-3, it makes an AP (iiI)

for the I, II, III eqns, form 3eqns in 3 variables and solve them to get the answer.

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