1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9


Question: 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.

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/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

S9 = (9/2) × [ 1 + 9 ] = 9/2 [10] = 9 × 5 = 45

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