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# What is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9?

The next number in the pattern can be identified by observing the relation between consecutive terms and their sum can be obtained by a formula.

## Answer: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

Let's observe the pattern.

**Explanation:**

The given sequence is 1, 2, 3, 4, 5, 6, 7, 8, 9. They are the first nine natural numbers.

The sum of first n natural numbers is n(n+1)/2

⇒ 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 9(9 + 1)/2 = 9 (10)/2 = 9 × 5 = 45

### ALTERNATE METHOD:

The common difference between the terms is 1. So, the next term is obtained by adding 1 to the previous number.

The given sequence is 1, 2, 3, 4, 5, 6, 7, 8, 9. They form an arithmetic progression.

\(S_n\)_{ }= n/2 × [ a + l] where a is the first term and l is the last term and n is the number of terms.

Here, n = 9, a = 1, l = 9

\(S_9\) = (9/2) × [ 1 + 9 ] = 9/2 [10] = 9 × 5 = 45

### Thus, 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

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