The next two terms if it is arithmetic are 19 and 28.
The next two terms if it is geometric are 100 and 1000.
The two possible next terms, if it is neither arithmetic nor geometric, are 27 and 52.
Given,
A sequence starts with the terms 1 and 10.
We need to find
- the next two terms if it is arithmetic: 1, 10,,.
- the next two terms if it is geometric: 1,10,.
What are the types of sequences?
Arithmetic sequence -A sequence where the difference between the consecutive term is the same.
The difference is called common difference denoted by d.
To find the nth term we use:
a_n = a + ( n - 1 ) d.
Geometric sequence - A sequence where each term is found by multiplying the preceding by a common ratio.
a_n = a_1 r^(n-1)
If 1, 10, , , is an arithmetic sequence.
a_1 = 1
d = 10 - 1 = 9
d = 9
a1 = 1
a2 = 10
a3 = 1 + ( 3 - 1 ) 9
a3 = 1 + 2 x 9 = 1 + 18 = 19
a3 = 19
a4 = a + ( 4 - 1 ) 9
a4 = 1 + 3 x 9 = 1 + 27 = 28
The given sequence is 1, 10, 19, 28.
If 1, 10, , , is a geometric sequence.
a_1 = 1
r = 10 / 1 = 10
a_n = a_1 r^(n-1)
a_3 = 1 x 10^(3-1)
a_3 = 10^2 = 100
a_4 = 1 x 10^(4-1)
a_4 = 10^3 = 1000
The given sequence is 1, 10, 100, 1000.
If 1, 10, , , is neither arithmetic nor geometric.
We can have,
(1 x 1) , (2 x 5), (3 x 9), (4 x 13)
1, 10, 27, 52
Thus,
The next two terms if it is arithmetic are 19 and 28.
The next two terms if it is geometric are 100 and 1000.
The two possible next terms, if it is neither arithmetic nor geometric, are 27 and 52
Learn more about sequences here:
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