Question

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.

Answer 1

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 + ….