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before explanation just a small amendment in ur question. instead of t(n)-t(n-1)-3, it should be t(n)-t(n-1) = -3

now it makes sense as it will take the shape of arithmatic progression.

please remember in arithmatic progression sequence difference between every consequitive number is fixed, and we call it D. in this case that fixed difference is -3 as given.

suppose A is the first number in the sequence, which is 23 in this case as given t(1) = 23.

Now nth term in the sequence will be A + (n-1)D,

we have t(n) = -4 = A+(n-1)D, putting the values from above we will get n = 10.