State whether the following sequence is arithmetic, geometric, or neither.
10, 10.25, 10.50625, 10.76890625, .... (Points : 1)
arithmetic sequence
geometric sequence
neither
1. check if 10.25-10 = 10.50625 - 10.25 , if true then AS
2. check if 10.25/10 = 10.50625/10.25 , if true then GS
if both are false, then "neither"
if one is true, verify with the other given value.
Arithmetic sequence
To determine whether the given sequence is arithmetic, geometric, or neither, we need to observe the pattern among the terms.
An arithmetic sequence is a sequence in which each term is obtained by adding a constant value, called the common difference, to the previous term. In other words, the difference between any two consecutive terms remains constant.
A geometric sequence is a sequence in which each term is obtained by multiplying a constant value, called the common ratio, by the previous term. In other words, the ratio between any two consecutive terms remains constant.
Let's analyze the given sequence:
10, 10.25, 10.50625, 10.76890625, ....
To determine if it is an arithmetic sequence, we need to check if the difference between consecutive terms is constant. Let's calculate the differences:
10.25 - 10 = 0.25
10.50625 - 10.25 = 0.25625
10.76890625 - 10.50625 = 0.26265625
As we can see, the differences are not constant. Therefore, the given sequence is not an arithmetic sequence.
To determine if it is a geometric sequence, we need to check if the ratio between consecutive terms is constant. Let's calculate the ratios:
10.25 / 10 = 1.025
10.50625 / 10.25 = 1.025
10.76890625 / 10.50625 ≈ 1.0249999
The ratios are approximately constant, but not exactly. Therefore, the given sequence is neither an arithmetic sequence nor a geometric sequence.
Hence, the correct answer is: neither.