Product of an AP?

Computer Science Level 2

$\large 1.6 \times 2.4 \times 3.2 \times \cdots \times 9.6$

The above represents the product of all the terms of an arithmetic progression . Express this product in the scientific form of notation.

Enter your answer as the sum of the integer part of the mantissa and exponent of the scientific notation.

For example, if your scientific notation is of the form $a \times 10^n$ , then enter your answer as $\lfloor a \rfloor + n$ .

Notation : $\lfloor \cdot \rfloor$ denotes the floor function .

The answer is 11.

1 solution

Arkajyoti Banerjee
Sep 29, 2016

Clearly, the above sequence is an Arithmetic Progression of $11$ terms with first term $1.6$ and common difference $0.8$ .

In order to find their product, I created a C++ program:

#include<iostream>
using namespace std;

int main()

{
    float a,d,p=1;
    int n,i=1; //i is the counting variable
    cout<<"Enter first term of the AP:"<<endl;
    cin>>a;
    cout<<"Enter common difference of the AP:"<<endl;
    cin>>d;
    cout<<"Enter number of terms of the AP:"<<endl;
    cin>>n;
    for(i=1;i<=n;i++,a=a+d)
        p=p*a;
    cout<<"Product="<<p;
    return 0;
}

Which on entering the required values, returned:

Mantissa: $4.1146 \implies \lfloor 4.1146 \rfloor = 4$

Exponent: $7$ .

Hence, $\lfloor a \rfloor + n = 4 + 7 = \boxed{11}$

Product of an AP?

The answer is 11.

1 solution

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