Question

What is the recursive formula for this geometric sequence4,-12,36,-108...

Answer 1

$a_{n+1}$ = - 3 $a_{n}$ with $a_{1}$ = 4

To find the next term in the sequence multiply the previous term by - 3

the common ratio r = $\frac{-108}{36}$ = $\frac{36}{-12}$ = - 3

$a_{n+1}$ = $a_{n}$ × r ← recursive formula

Answer 2

Answer: $a_{n+1}=-3a_{n}$

Step-by-step explanation:

The recursive formula for geometric sequence is given by :-

$a_{n+1}=a_{n}r$  -----(1) , where r = common ratio and n=natural number .

nth term of geometric sequence = $ar^{n-1}$

The given geometric sequence : 4,-12,36,-108...

First term = $a_1=a=4$

Second term =  $a_2=ar=-12$

Also, $r=\dfrac{ar}{a}=\dfrac{-12}{4}=-3$

∴ r = -3

Put the value of r in (1) , we get the recursive formula for given geometric sequence  as

$a_{n+1}=a_{n}(-3)$

i.e. $a_{n+1}=-3a_{n}$