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Question

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

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Solution

The n th term of the sequence is given as,

a n =3 a n1 +2(1)

And it is given that a 1 =3.

Substitute n=2 in equation (1),

a 2 =3 a 21 +2 =3 a 1 +2 =3( 3 )+2 =11

Substitute n=3 in equation (1),

a 3 =3 a 31 +2 =3 a 2 +2 =3( 11 )+2 =35

Substitute n=4 in equation (1),

a 4 =3 a 41 +2 =3 a 3 +2 =3( 35 )+2 =107

Substitute n=5 in equation (1),

a 5 =3 a 51 +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+


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