Write the first five terms of each of the sequences in and obtain the corresponding series:
a1 = 3, an = 3an – 1 + 2 for all n > 1
Given here are a1 = 3,
an = 3a(n – 1) + 2…………1
To find out first five terms of the sequence we will put value of n = 2, 3, 4, 5 in 1
a2= 3(3)2-1 + 2 = 3 × 3 + 2 = 11
a3 = 3a2 + 2 = 3 × 11 + 2 = 35 (∵ an-1 = a3-1 = a2 )
a4 = 3a3 + 2 = 105 + 2 = 107
a5 = 3a4 + 2 = 3 × 107 + 2 = 323
Hence the first five terms of the sequence are 3, 11, 35, 107, 323
And the corresponding sequence is 3 + 11 + 35 + 107 + 323 + …….