Answer :
The explicit formula for given sequence is: [tex]a_n = -1 . (-4)^{n-1}[/tex]
Step-by-step explanation:
Given sequence is:
-1,4,-16,64.....
We can see that there is no same difference between consecutive terms so we will find common ratio to see if it is a geometric sequence.
Here
[tex]a_1 = -1\\a_2 = 4\\a_3 = -16\\a_4 = 64\\r = \frac{a_2}{a_1} = \frac{4}{-1} = -4\\r = \frac{a_3}{a_2} = \frac{-16}{4} = -4[/tex]
The explicit formula for geometric sequence is:
[tex]a_n = a_1r^{n-1}[/tex]
Putting the values of r and a1
[tex]a_n = -1 . (-4)^{n-1}[/tex]
Hence
The explicit formula for given sequence is: [tex]a_n = -1 . (-4)^{n-1}[/tex]
Keywords: Geometric sequence, common ratio
Learn more about geometric sequence at:
- brainly.com/question/4767370
- brainly.com/question/4770453
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