A geometric sequence is defined by the following formula a_n = a_0 r^n-1 This ca

Question

A geometric sequence is defined by the following formula a_n = a_0 r^n-1 This can also be written using the recursive relation: Where a_n represents the n-th term in the sequence. For example, the sequence a_n = 1/2 a_n-1 with a_0 = 10 is given by 10, 5, 5/2, 5/4,... Create a class Geometric Sequence with the following methods: geometric Sequence that takes three parameters: aNaught the first element of the sequence (i.e. a_0) ratio: the ratio to multiply by (i.e.r) index: the index of the term in the sequence to find (i.e.n) and finds n-th term in the sequence using the closed form (i.e. non-recursive) formula. geometric sequence Recursive that takes the same three parameters, but uses the second definition to the find the solution recursively. In a addition geometric Sequence Recursive should print a stack trace to show how many steps were required to an at the solution. It must only print the stack trace once, at the deepest level of recursion. You may use the following method to print the stack trace:

Explanation / Answer

Ans;

public class GeometricSequence{

    public static void main(String[] args) {

int a0,n,r;

System.out.println(" Enter aNaught: the first element of the sequence (i.e. a0)");

a0 = in.nextInt();

System.out.println(" Enter ratio: the ratio to multiply by (i.e. r)");

r = in.nextInt();

System.out.println(" Enter index: the index of the term in the sequence to find (i.e. n)");

n = in.nextInt();

geometricSequence(a0,r,n);

}

public static void geometricSequence(int a0,int r, int n){

for(int i=1;i<=n;i++)

{a=a0*(Math.pow(r,(i-1)));

}

}

public static void geometricSequenceRecursive (int a0,int r, int n)

if(n>=1)

{

System.out.println( +n+ . +printStackTrace());

a=r* geometricSequenceRecursive(a0,r,(n-1));

}

else

{ System.out.println ( . . .);

System.out.println ( +a);

}

}}

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