Make and test a conjecture about the sum of numbers from 1 to 7. Write a conjecture for the general case.

The correct answer is: (n2 + n)/2

 A sequence of numbers which has a common difference between any two consecutive numbers is called an arithmetic progression (A.P.). The arithmetic progression general form is given by a, a + d, a + 2d, a + 3d, . . .. Hence, the formula to find the nth term is:

a_n = a + (n – 1) × d
To find the sum of arithmetic progression, we have to know the first term, the number of terms and the common difference between each term. Then use the formula given below:

S = n/2[2a + (n − 1) × d]
Sum of numbers from 1 to 7
The first n natural numbers are given by 1,2,3,4,5,6,7…… (n) and this forms an AP.

• a = 1
• d = 1
• t_n = n

The formula of sum of an A.P series

S = n/2[2a + (n − 1) × d]

S = n /2 [2 + n – 1]

S = n /2 [n+1]

S = (n² + n)/2
The sum of first n natural numbers is (n² + n)/2