Which of the following best describes this sequence? $$ \{1,3,6,10,15,21, \ldots\} $$ Arithmetic Geometric Both Neither

Question

UpStudy AI · Accepted Answer

To analyze the sequence {1, 3, 6, 10, 15, 21, …}, we first look at the differences between successive terms:

• 3 - 1 = 2  
• 6 - 3 = 3  
• 10 - 6 = 4  
• 15 - 10 = 5  
• 21 - 15 = 6

Since the differences are not constant, the sequence is not arithmetic.

Next, for a geometric sequence, the ratio between successive terms should be constant. Checking the ratios:

• 3 / 1 = 3  
• 6 / 3 = 2  
• 10 / 6 ≈ 1.67  
• 15 / 10 = 1.5  
• 21 / 15 = 1.4

Since these ratios are not equal, the sequence is not geometric either.

Therefore, the correct answer is: Neither.
The sequence is neither arithmetic nor geometric.

Which of the following best describes this sequence? \( \{1,3,6,10,15,21, \ldots\} \) Arithmetic Geometric Both Neither