Find the first five terms of the sequence in which a1 = 6 and an = –3an – 1 – 12, if n ≥ 2.

ANSWER

EXPLANATION

The given sequence is defined recursively by:

This means that the subsequent terms of the sequence are generated by multiplying the previous term by -3. This will therefore generate a geometric sequence.

When n=2,

To generate the next term in this geometric sequence, we multiply -18 by -3.

To get the fourth term, multiply 54 by -3.

To get the 5th term we multiply -162 by -3.

Therefore the first five terms are:

10a^3+277a^2-132a-792

step-by-step explanation:

(2a+11)(5a-12)(foil)

=10a^2-24a+55a-132 =10a^2+31a-132

(10a^2+31a-132)(a+6)

=10a^3+60a^2+31a^2+186a^2-132a-792 =10a^3+277a^2-132a-792

i hope this is what you are looking for : )