The condition for which three numbers (a,b,c) are in A.G.P is? thank you
Any (a,b,c) are in arthmetic-geometric progression
Arithmetic geometric progression means that getting from one number to the next involves multiplying by a constant then adding a constant, i.e. if we are at
This means we have formulae for
If we're given a specific
Plugging this into the equation for
Therefore, given ANY
This can be stated in another way. There are three "degrees of freedom" for any arithmetico-geometric progression: the initial value, the multiplied constant, and the added constant. Therefore, it takes three values exactly to determine what A.G.P. is applicable.
A geometric series, on the other hand, only has two: the ratio and the initial value. This means it takes two values to see exactly what geometric sequence is and that determines everything afterwards.
No such condition.
In an arithmetic geometric progression, we have term-by-term multiplication of a geometric progression with the corresponding terms of an arithmetic progression, such as
If three terms are
and given three terms and three equations,
solving for four terms is generally not possible and relation depends more on specific values of