Here, we are required to find the next two numbers of the sequence; 2, 3, 4.5, 6.75, _, _
The sequence which is requires is;
- 2, 3, 4.5, 6.75, 10.125, 15.1875
While finding an expression that defines a sequence, such as a geometric progression as given in the question, we are required to find;
- The first term of the progression, a;
- and the common ratio, r.
However, since the question only requires that the next two terms be found, we only need to find the common ratio of the sequence:
Common ratio, r = T2/T1 = T3/T2 = T4/T3
Therefore, from the question above;
r = 3/2 = 4.5/3 = 6.75/4.5 = 1.5
Therefore common ratio = 1.5
To find the next term; we multiply 6.75 by 1.5
Therefore, next term is, T5 = 10.125
And to find the next term after 10.125, we multiply 10.125 by 1.5;
and ultimately, we have 15.1875.
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https://brainly.com/question/12998719
