A sequence is given by the recursive rule \(t_1 = 2, t_{n+1} = 3t_n − 2\) for \(n ≥ 1\). Which term of the sequence is 730?

SOLUTION

Generate the terms using the recursive rule
\(t_1 = 2\)
\(t_2 = 3(2) − 2 = 4\)
\(t_3 = 3(4) − 2 = 10\)
\(t_4 = 3(10) − 2 = 28\)
\(t_5 = 3(28) − 2 = 82\)
\(t_6 = 3(82) − 2 = 244\)
\(t_7 = 3(244) − 2 = 730\)
So, 730 is the \(7^{th}\) term.

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Final Answer : 730 is the \(7^{th}\) term.

Concept Note

A recursive sequence defines each term using the previous terms.
Here, \(t_{n+1} = 3t_n − 2\)
To find a particular term, repeatedly apply the rule until the required value appears.