Question

Find the first five terms of the recursive sequence an=-6an-1 where a1=4.5

Answer 1

Answer:

4.5, -27, 162,-972, 5832

Step-by-step explanation:

The given recursive definition is,

$a_n=-6a_{n-1}, a_1=4.5$

This will form a geometric sequence with first term 4.5 and common ratio r=-6.

When n=2, we have:

$a_2=-6a_1 \\ \implies \: a_2=-6 \times 4.5 = - 27$

When n=3, we get:

$a_3=-6a_2 \\ \implies \: a_3=-6 \times - 27 = 162$

When n=4, we get:

$a_4=-6a_3 \\ \implies \: a_4=-6 \times 162 = - 972$

When n=5, we get:

$a_5=-6a_4 \\ \implies \: a_5=-6 \times - 972 = 5832$

Therefore the first five terms are:

4.5, -27, 162,-972, 5832