Question

Complete the recursive formula of the geometric sequence -1.5\,,\,6\,,-24\,,\,96,...−1.5,6,−24,96,...minus, 1, point, 5, comma, 6, comma, minus, 24, comma, 96, comma, point, point, point.
d(1)=d(1)=d, left parenthesis, 1, right parenthesis, equals


d(n)=d(n-1)\cdotd(n)=d(n−1)⋅d, left parenthesis, n, right parenthesis, equals, d, left parenthesis, n, minus, 1, right parenthesis, dot

Answer 1

Answer:

$d(1)=-1.5$  and recursive formula is $d(n)=d(n-1)\cdot (-4)$.

Step-by-step explanation:

The given geometric sequence is

$-1.5, 6, -24, 96,...$

Here, the first term is -1.5. So

$d(1)=-1.5$

Second term is 6. So,

$d(2)=6$

In the given geometric sequence, the common ratio is

$r=\dfrac{d(2)}{d(1)}=\dfrac{6}{-1.5}=4$

The recursive formula of the geometric sequence is

$d(n)=d(n-1)\cdot r$

where r is common ratio.

$d(n)=d(n-1)\cdot (-4)$

Therefore, the recursive formula is $d(n)=d(n-1)\cdot (-4)$.