## An arithmetic progression is a sequence of numbers in which the distance (or difference) between any two successive numbers if the same. Thi

Question

An arithmetic progression is a sequence of numbers in which the distance (or difference) between any two successive numbers if the same. This in the sequence 1, 3, 5, 7, …, the distance is 2 while in the sequence 6, 12, 18, 24, …, the distance is 6. Given the positive integer distance and the positive integer n, associate the variable sum with the sum of the elements of the arithmetic progression from 1 to n with distance distance. For example, if distance is 2 and n is 10, then sum would be associated with 25 because 1+3+5+7+9 = 25.

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3 weeks 2021-09-24T04:02:15+00:00 2 Answers 0

Step-by-step explanation:

Solution:

– We are to write a program for evaluating the sum to Nth of an arithmetic sequence such that the sequence starts from positive integer 1, 3 , 5 , 7 , .. n.

– The sum to nth for the arithmetic series is given by two parameters i.e first integer a = 1 and the distance between successive integers d = 2 in our case.

– For any general distance d we can write our sum to nth as:

Sum to nth = a + (a+d) + (a+2*d) + (a+3*d) …. (a + (n-1)*d)

– From above sequence we can see that every successive number is increased by distance d and added in previous answer.

– We will use an iteration loop for a variable “sum”, which is cycled by a “range ( , , )” function.

– The parameters of the range functions corresponds to:

range ( first integer , last integer , step size )

range ( a , n + 1 , d )

– Then we can cast the loop as follows:

” int sum = 0

int d = 2

int a = 1

for i in range ( a , n + 1 , d )

sum += i

”

– We see that iteration parameter i starts from a = 1, with step size d = 2 and the sum is previously stored sum value plus i for the current loop.

def arithmetic (n, dist):

sum = 0

for num in range(1, n + 1, dist):

sum += num

print(sum)

arithmetic(10, 2)

Step-by-step explanation:

The question asked us to write a program given the positive integer n, and positive integer distance and then associate the variable sum with the sum of the elements of the arithmetic progression from 1 to n with distance.

using python the code can be written as:

def arithmetic (n, dist):

I wrote a function that accept 2 argument n the positive integer and the distance , dist.

sum = 0

The sum is equal to 0 at the beginning.

for num in range(1, n + 1, dist):

The code loop through the number in the range of 1 to the n value with a distance value.

sum += num

The looped value are then added to the sum value to get the sum.

print(sum)

The sum are printed

arithmetic(10, 2)

The function is called and filled with the required argument . In our case the positive integer n is inputted and the distance value.