Question

Find the 9 th term in the following sequence whose n th term is

Answer 1

The n th term of the sequence is given as,

a n =3 a n−1 +2(1)

And it is given that a 1 =3.

Substitute n=2 in equation (1),

a 2 =3 a 2−1 +2 =3 a 1 +2 =3( 3 )+2 =11

Substitute n=3 in equation (1),

a 3 =3 a 3−1 +2 =3 a 2 +2 =3( 11 )+2 =35

Substitute n=4 in equation (1),

a 4 =3 a 4−1 +2 =3 a 3 +2 =3( 35 )+2 =107

Substitute n=5 in equation (1),

a 5 =3 a 5−1 +2 =3 a 4 +2 =3( 107 )+2 =323

The required first five terms are 3,11,35,107,323.

The corresponding series will be,

3+11+35+107+323+⋯