t100=t99+1=(tn)(tn)-1

Need more information on what to do given these equal statements.

If t_n = n-1 then t₉₉ = 98,  t₁₀₀ = 99 (= t₉₉ + 1) and t₁₁ = 10 so that t₁₁² - 1 = 99 (= t₁₀₀)

Where did you get     $$t_{11}$$    from Alan?

I am completely lost. lol. 

Some things in life are meant to be a mystery.  Is this one on those?  

Think of this as a function t(n) = n - 1

t(1) = 0

t(2) = 1

t(3) = 2

...

t(10) = 9

t(11) = 10

...

t(99) = 98

t(100) = 99

Clearly t(100) = 99 = 98 + 1 = t(99) + 1

Also t(11)² - 1 = 10² -1 = 99 = t(100) = t(99) + 1

I'm not sure I'd classify this as one of life's great mysteries!!

Thanks Alan,

I will think more about it when I am less tired.