Question

for each sequence: a. state if it is arithmetic, geometric, or neither. given an arithmetic or geometric sequence (if the sequence is neither arithmetic nor geometric, skip part b). b. given an arithmetic or geometric sequence, write the equation. 1. 1, 3, 6, 10, 15, ... a. b. equation:

Explanation:

Step1: Check if arithmetic

Find the differences between consecutive terms. For the sequence 1, 3, 6, 10, 15, ..., the differences are \(3 - 1=2\), \(6 - 3 = 3\), \(10 - 6=4\), \(15 - 10 = 5\). Since the differences are not constant, it is not an arithmetic sequence.

Step2: Check if geometric

Find the ratios between consecutive terms. The ratios are \(\frac{3}{1}=3\), \(\frac{6}{3}=2\), \(\frac{10}{6}=\frac{5}{3}\), \(\frac{15}{10}=\frac{3}{2}\). Since the ratios are not constant, it is not a geometric sequence.

Answer:

Neither arithmetic nor geometric.