Question

In a geometric sequence, a2= -144 and a5=486. Write the explicit formula for this sequence

Answer 1

Answer:

$a_{n}$ = 96$(-1.5)^{n-1}$

Step-by-step explanation:

The n th term of a geometric sequence is

$a_{n}$ = a$(r)^{n-1}$

where a is the first term and r the common ratio.

Both values have to be found.

Using

a₂ = - 144, then

ar = - 144 → (1)

a₅ = 486, then

a$r^{4}$ = 486 → (2)

Divide (2) by (1)

$\frac{ar^4}{ar}$ = $\frac{486}{-144}$

r³ = - 3.375 ( take the cube root of both sides )

r = - 1.5

Substitute r = - 1.5 into (1)

- 1.5a = - 144 ( divide both sides by - 1.5 )

a = 96

Hence explicit formula is

$a_{n}$ = 96$(-1.5)^{n-1}$