Find tn of the A.P.: 3, 6, 9, ....

Answer

For an Arithmetic Progression (A.P.), the formula for the n-th term is given by: $$t_n = a + (n - 1)d$$ Where \(a\) is the first term and \(d\) is the common difference.

In this sequence, the first term is \(a = 3\). The common difference is calculated by subtracting the first term from the second term: $$d = t_2 - t_1 = 6 - 3 = 3$$

Now, we substitute the values of \(a\) and \(d\) into the formula: $$t_n = 3 + (n - 1)3$$

By expanding the expression, we get: $$t_n = 3 + 3n - 3$$

Finally, simplifying the expression gives the n-th term: $$t_n = 3n$$