Find the first four terms of the sequence defined by a_1=3 and a_… - Vidyadip

Question

Find the first four terms of the sequence defined by $\text{a}_1=3$ and $\text{a}_\text{n}=3\text{a}_{\text{n}-1}+2$ for all $\text{n}>1.$

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Answer

$\text{a}_\text{n}=3\text{a}_{\text{n}-1}+2$ $\text{a}_1=3$ $\text{a}_1=\text{3a}_{2-1}+2=\text{3a}_{2-1}+2=3(3)+2=11$ $\text{a}_3=\text{3a}_{3-1}+2=3\text{a}_2+2=3(11)+2=35$ $\text{a}_4=\text{3a}_{4-1}+2=\text{3a}_3+2=3(35)+2=107$ First four terms of the sequence are 3, 11, 35 and 107.

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