Verbally describe this pattern
1,3,6,10,15,21
The nth term is the sum of the first n positive integers.
Or, starting with 1, add 1. Then increase the amount added by 1 for each term. That is, the next amounts added are
2,3,4,5,...
add the last two numbers in the begining add 1 three times
To verbally describe the pattern 1, 3, 6, 10, 15, 21, we observe that each number is obtained by adding the next natural number in sequence to the previous number.
Let's break it down step by step:
The first number in the sequence is 1.
The second number is obtained by adding 2 to the previous number (1 + 2 = 3).
The third number is obtained by adding 3 to the previous number (3 + 3 = 6).
The fourth number is obtained by adding 4 to the previous number (6 + 4 = 10).
The fifth number is obtained by adding 5 to the previous number (10 + 5 = 15).
The sixth number is obtained by adding 6 to the previous number (15 + 6 = 21).
So, the pattern is generated by the formula: n(n+1)/2, where n represents the position of each number in the sequence.
For example,
- The first number (n = 1) is 1(1+1)/2 = 1.
- The second number (n = 2) is 2(2+1)/2 = 3.
- The third number (n = 3) is 3(3+1)/2 = 6.
- The fourth number (n = 4) is 4(4+1)/2 = 10.
- The fifth number (n = 5) is 5(5+1)/2 = 15.
- The sixth number (n = 6) is 6(6+1)/2 = 21.
So, the pattern can be described as a sequence of numbers obtained by adding each natural number in sequence to the previous number.