Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series: a1 = 3, an = 3an – 1 + 2 for all n > 1.
Solution and Explanation
a1 = 3, an = 3an-1 +2 for all n>1
⇒ a2 = 3a1 + 2 = 3(3) + 2 = 11
a3 = 3a2 +2 = 3(11) + 2 =35
a4 = 3a3+2 = 3(35) + 2 = 107
a5 = 3a4+2 = 3(107) + 2 = 323
Hence, the first five terms of the sequence are 3, 11, 35, 107, and 323.
The corresponding series is 3 + 11 + 35 + 107 + 323 + ….
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