Maths-

General

Easy

Question

# 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 = (n^{2 }+ n)/2

The sum of first n natural numbers is (n^{2 }+ n)/2

_{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:

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.

_{n}= n^{2 }+ n)/2

The sum of first n natural numbers is (n

^{2 }+ n)/2

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