Question

1, 3, 6, 10, 15 is it arithmetic, geometric or neither

Answer 1

The given sequence is neither arithmetic nor geometric.

Further explanation:

In order to check whether a sequence is geometric or arithmetic we have to find the common ratio and common difference respectively

Common difference is the deifference between cunsecutive terms of a sequence while common ratio is the ratio between two consecutive terms.

Common difference is denoted by d and common ratio is denoted by r

• If the common difference is same then the given sequence is an arithmetic sequence
• If the common ratio is same then the given sequence is a geometric sequence

Given

1, 3, 6, 10, 15

Common difference:

Here

$a_1=1\\a_2=3\\a_3=6\\a_4=10\\a_5=15\\Common\ Difference=a_2-a_1=3-1=2\\a_3-a_2=6-3=3\\a_4-a_3=10-6=4$

As the common difference is not same, the given sequence is not an arithmetic sequence

Common Ratio:

$r=\frac{a_2}{a_1}=\frac{3}{1}=3\\\frac{a_3}{a_2}=\frac{6}{3}=2\\\frac{a_4}{a_3}=\frac{10}{6}=1.6$

As the common ratio is also not same the sequence is not a geometric sequence.

The given sequence is neither arithmetic nor geometric.

Keywords: Arithmetic sequence, Geometric Sequence

Learn more about sequences at:

• brainly.com/question/12597153
• brainly.com/question/12685192

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