Question

What is the recursive formula for this geometric sequence?

2,-10, 50, -250, ...
=
O A. (2
O B.
O C.
an = 3n-1 (-5)
(a₁ = 2
an = an-1.5
(2₁ = -5
Lan
an = an-1.2
O D. (²8)
= 2
= 8-1 (-8)

Answer 1

The recursive formula for the geometric sequence 2, -10, 50, -250, ... is an = an-1 × -5, given that the first term is 2.

Step-by-step explanation:

The recursive formula for the given geometric sequence 2, -10, 50, -250, ... can be determined by looking at the ratio between consecutive terms. The ratio is obtained by dividing a term by its preceding term. For instance, if we divide -10 by 2, we get -5, and similarly, dividing 50 by -10 also results in -5. This indicates that the common ratio (r) is -5. A recursive formula for a geometric sequence is generally given by an = an-1 × r, where an is the nth term and an-1 is the term before it. Hence, the recursive formula for this sequence, given that the first term (a1) is 2, can be written as an = an-1 × -5.