Chemistry - Acidity of cyclopentadiene when fused to benzene rings

Clar's rule states that (Solà, 2013):

The Kekulé resonance structure with the largest number of disjoint aromatic π-sextets, i.e., benzene-like moieties, is the most important for characterization of properties of polycyclic aromatic hydrocarbons (PAHs).

Applying Clar's rule to the the question, we would realise that in the indenyl and fluorenyl anions, the resonance structures where there are 6 π-electrons delocalised exclusively within the fused benzene rings would contribute more to the actual structure than the resonance structures where the π-electrons are delocalised along the 5-membered ring. In the major resonance structure for the fluorenyl anion, we would have the negative charge concentrated on the carbon atom, without delocalisation.

In the cyclopentadienyl anion, the negative charge is completely delocalised, as shown below in the resonance structures. Thus, it is the most stable among them. In the indenyl and fluorenyl anions, the negative charge is not as delocalised and thus, these are less stable.

Due to this, the π-electrons in the 5-membered ring experiences the most delocalisation and achieves most aromatic stabilisation in the cyclopentadienyl anion, and this gradually decreases going to the indenyl and fluorenyl anions.

Reference

Solà, M. (2013). Forty years of Clar's aromatic π-sextet rule. Frontiers in Chemistry, 1(22). doi:10.3389/fchem.2013.00022