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
Given
1, 3, 6, 10, 15
Common difference:
Here
[tex]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[/tex]
As the common difference is not same, the given sequence is not an arithmetic sequence
Common Ratio:
[tex]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[/tex]
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
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