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An AP consists of 50 terms in which the \(3^{rd}\) term is 12 and the last term is 106. Find the \(29^{th}\) term.
(Hint: If 'a' is the first term and 'd' the common difference, then we arrive at the equations a + 2d = 12 and a + 49d = 106. Solve this pair of linear equations for 'a' and 'd'.)

Find the \(n^{th}\) term of the AP: 11, 8, 5, 2,... Write the recursive rule for this AP.

Which term of the AP: 21, 18, 15,... is −81? Also, is 0 a term of this AP? Give reasons for your answer.

Find the \(10^{th}\) and \(26^{th} \) terms of the AP: 3, 8, 13, 18,...

Let \(T_1 = 1, T_2 = 2, T_3 = 4, \,and\, T_n = T_{n−1} + T_{n−2} + T_{n−3}\) for n ≥ 4. Find \(T_4, T_5, T_6, T_7,\,and\, T_8\).

A sequence is given by the recursive rule \(t_1 = −5, t_{n+1} = t_n + 3\) for \(n ≥ 1\). Find the first five terms of the sequence. Is 52 a term of this sequence? If so, which term is it?

Which term of the sequence \(t_n = 5n − 3\) for \(n ≥ 1\) is 607?

Determine whether 97 and 172 are terms of the sequence \(t_n = 5n − 3\) for \(n ≥ 1\).

Find the \(10^{th}\) and \(15^{th}\) terms of the sequence \(t_n = 5n − 3\) for \(n ≥ 1\).

Find the first five terms of the sequence in which the \(n^{th}\) term is given by \(t_n = n^2 − 2n + 3\) for \(n ≥ 1\).