Answer:
A)2,6,10
B)2,-6,-18
C)-1,-3,-5
Step-by-step explanation:
A)a1=-2 and d=4
We know that the arithmetic sequence formula is
[tex]a_{n}=a_{1}+(n-1)d[/tex]
Now
[tex]a_{2}=a_{1}+(2-1)d[/tex]
[tex]a_{2}=a_{1}+(1)d[/tex]
Substituting the given value we get
[tex]a_{2}= -2+(1)4[/tex]
[tex]a_{2}= -2+4[/tex]
[tex]a_{2}= 2[/tex]
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Similarly
[tex]a_{3}=a_{1}+(3-1)d[/tex]
[tex]a_{3}=a_{1}+(2)d[/tex]
Substituting the given value we get
[tex]a_{3}= -2+(2)4[/tex]
[tex]a_{3}= -2+8[/tex]
[tex]a_{3}= 6[/tex]
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[tex]a_{4}=a_{1}+(4-1)d[/tex]
[tex]a_{4}=a_{1}+(3)d[/tex]
Substituting the given value we get
[tex]a_{4}= -2+(3)4[/tex]
[tex]a_{4}= -2+16[/tex]
[tex]a_{4}= 10[/tex]
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B [tex]a_n=a_{(n-1)}-8[/tex] with [tex]a_1=10[/tex]
[tex]a_2=a_{(2-1)}-8[/tex]
[tex]a_2=a_{1}-8[/tex]
Substituting the given value
[tex]a_2= 10-8[/tex]
[tex]a_2=2[/tex]
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[tex]a_3=a_{(3-1)}-8[/tex]
[tex]a_3=a_{2}-8[/tex]
Substituting the value
[tex]a_3=2-8[/tex]
[tex]a_3= -6[/tex]
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[tex]a_4=a_{(4-1)}-8[/tex]
[tex]a_4=a_{3}-8[/tex]
Substituting the value
[tex]a_4= -6-8[/tex]
[tex]a_4= -14[/tex]
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C) [tex] a_1=3, a_2=1[/tex]
Here the difference is -2
the arithmetic sequence formula is
[tex]a_{n}=a_{1}+(n-1)d[/tex]
Now
[tex]a_{3}=a_{1}+(3-1)d[/tex]
[tex]a_{3}=a_{1}+(2)d[/tex]
Substituting the value we get
[tex]a_{3}= 3+(2)-2[/tex]
[tex]a_{3}= 3-4[/tex]
[tex]a_{3}= -1[/tex]
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[tex]a_{4}=a_{1}+(4-1)d[/tex]
[tex]a_{4}=a_{1}+(3)d[/tex]
Substituting the value we get
[tex]a_{4}= 3+(3)-2[/tex]
[tex]a_{4}= 3-6[/tex]
[tex]a_{4}= -3[/tex]
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[tex]a_{5}=a_{1}+(5-1)d[/tex]
[tex]a_{5}=a_{1}+(4)d[/tex]
Substituting the value we get
[tex]a_{5}= 3+(4)-2[/tex]
[tex]a_{5}= 3-8[/tex]
[tex]a_{5}= -5[/tex]
The next three terms of each of the arithmetic sequence shown is obtained as:
An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
[tex]a, a + d, a + 2d, ... , a + (n+1)d, ...[/tex]
Its nth term is
[tex]T_n = a + (n-1)d[/tex]
(for all positive integer values of n)
And thus, the common difference is
[tex]T_{n+1} -T_n[/tex]
for all positive integer values of n
For the given sequences, the next three terms are obtained as:
The first term is 2, and difference is 4, thus, next three terms would be:
2+4, 2+4 + 4, 2 + 4 + 4 + 4
or
6, 10, 14
Since to obtain next term, we need to subtract 8, thus, the value of 'd' is -8
The first term is 10, therefore, the next three terms are:
[tex]10 - 8, 10 -8 - 8, 10 - 8 - 8 - 8[/tex]
or
2, -6, -14
The first term is 2 extra than second term. That means, there's decrement in each next term, of 2 units. Thus, d = - 2
Therefore, the next 3 terms are:
[tex]a_3 = a_2 +d = 1 - 2 = -1\\a_4 = a_3 + d = -1 - 2 = -3\\a_5 = a_4 + d = -3 - 2 = -5[/tex]
Therefore, the next three terms of each of the arithmetic sequence shown is obtained as:
Learn more about arithmetic sequence here:
https://brainly.com/question/3702506
