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garik1379 [7]
3 years ago
15

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

Mathematics
2 answers:
Natalka [10]3 years ago
7 0

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




Karolina [17]3 years ago
5 0

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}

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