Find an expression for the nth term (t_n) in each of the following

A sequence is given to us is , and we need to find expression for nth term of the sequence. The given sequence is ,

When we flip the numbers , we can clearly see that the number are in Harmonic Progression.

That is when we flip the numbers they are found to be in Arithmetic Progression .

And nth term of an Harmonic Progression is :-

Hence here

Substituting the respective values,

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1