Answer:
A)2,6,10
B)2,-6,-18
C)-1,-3,-5
Step-by-step explanation:
<u>A)a1=-2 and d=4</u>
We know that the arithmetic sequence formula is
![a_{n}=a_{1}+(n-1)d](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7B1%7D%2B%28n-1%29d)
Now
![a_{2}=a_{1}+(2-1)d](https://tex.z-dn.net/?f=a_%7B2%7D%3Da_%7B1%7D%2B%282-1%29d)
![a_{2}=a_{1}+(1)d](https://tex.z-dn.net/?f=a_%7B2%7D%3Da_%7B1%7D%2B%281%29d)
Substituting the given value we get
![a_{2}= -2+(1)4](https://tex.z-dn.net/?f=a_%7B2%7D%3D%20-2%2B%281%294)
![a_{2}= -2+4](https://tex.z-dn.net/?f=a_%7B2%7D%3D%20-2%2B4)
![a_{2}= 2](https://tex.z-dn.net/?f=a_%7B2%7D%3D%202)
------------------------------------------
Similarly
![a_{3}=a_{1}+(3-1)d](https://tex.z-dn.net/?f=a_%7B3%7D%3Da_%7B1%7D%2B%283-1%29d)
![a_{3}=a_{1}+(2)d](https://tex.z-dn.net/?f=a_%7B3%7D%3Da_%7B1%7D%2B%282%29d)
Substituting the given value we get
![a_{3}= -2+(2)4](https://tex.z-dn.net/?f=a_%7B3%7D%3D%20-2%2B%282%294)
![a_{3}= -2+8](https://tex.z-dn.net/?f=a_%7B3%7D%3D%20-2%2B8)
![a_{3}= 6](https://tex.z-dn.net/?f=a_%7B3%7D%3D%206)
-------------------------------------------------
![a_{4}=a_{1}+(4-1)d](https://tex.z-dn.net/?f=a_%7B4%7D%3Da_%7B1%7D%2B%284-1%29d)
![a_{4}=a_{1}+(3)d](https://tex.z-dn.net/?f=a_%7B4%7D%3Da_%7B1%7D%2B%283%29d)
Substituting the given value we get
![a_{4}= -2+(3)4](https://tex.z-dn.net/?f=a_%7B4%7D%3D%20-2%2B%283%294)
![a_{4}= -2+16](https://tex.z-dn.net/?f=a_%7B4%7D%3D%20-2%2B16)
![a_{4}= 10](https://tex.z-dn.net/?f=a_%7B4%7D%3D%2010)
-------------------------------------------------------------------------------------------
<u>B</u><u>
with
</u>
![a_2=a_{(2-1)}-8](https://tex.z-dn.net/?f=a_2%3Da_%7B%282-1%29%7D-8)
![a_2=a_{1}-8](https://tex.z-dn.net/?f=a_2%3Da_%7B1%7D-8)
Substituting the given value
![a_2= 10-8](https://tex.z-dn.net/?f=a_2%3D%2010-8)
![a_2=2](https://tex.z-dn.net/?f=a_2%3D2)
---------------------------------------------------------------------
![a_3=a_{(3-1)}-8](https://tex.z-dn.net/?f=a_3%3Da_%7B%283-1%29%7D-8)
![a_3=a_{2}-8](https://tex.z-dn.net/?f=a_3%3Da_%7B2%7D-8)
Substituting the value
![a_3=2-8](https://tex.z-dn.net/?f=a_3%3D2-8)
![a_3= -6](https://tex.z-dn.net/?f=a_3%3D%20-6)
---------------------------------------------------------------------
![a_4=a_{(4-1)}-8](https://tex.z-dn.net/?f=a_4%3Da_%7B%284-1%29%7D-8)
![a_4=a_{3}-8](https://tex.z-dn.net/?f=a_4%3Da_%7B3%7D-8)
Substituting the value
![a_4= -6-8](https://tex.z-dn.net/?f=a_4%3D%20-6-8)
![a_4= -14](https://tex.z-dn.net/?f=a_4%3D%20-14)
-------------------------------------------------------------------------------------------
<u>C)
</u>
Here the difference is -2
the arithmetic sequence formula is
![a_{n}=a_{1}+(n-1)d](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7B1%7D%2B%28n-1%29d)
Now
![a_{3}=a_{1}+(3-1)d](https://tex.z-dn.net/?f=a_%7B3%7D%3Da_%7B1%7D%2B%283-1%29d)
![a_{3}=a_{1}+(2)d](https://tex.z-dn.net/?f=a_%7B3%7D%3Da_%7B1%7D%2B%282%29d)
Substituting the value we get
![a_{3}= 3+(2)-2](https://tex.z-dn.net/?f=a_%7B3%7D%3D%203%2B%282%29-2)
![a_{3}= 3-4](https://tex.z-dn.net/?f=a_%7B3%7D%3D%203-4)
![a_{3}= -1](https://tex.z-dn.net/?f=a_%7B3%7D%3D%20-1)
------------------------------------------------------------------------------
![a_{4}=a_{1}+(4-1)d](https://tex.z-dn.net/?f=a_%7B4%7D%3Da_%7B1%7D%2B%284-1%29d)
![a_{4}=a_{1}+(3)d](https://tex.z-dn.net/?f=a_%7B4%7D%3Da_%7B1%7D%2B%283%29d)
Substituting the value we get
![a_{4}= 3+(3)-2](https://tex.z-dn.net/?f=a_%7B4%7D%3D%203%2B%283%29-2)
![a_{4}= 3-6](https://tex.z-dn.net/?f=a_%7B4%7D%3D%203-6)
![a_{4}= -3](https://tex.z-dn.net/?f=a_%7B4%7D%3D%20-3)
----------------------------------------------------------------------------------
![a_{5}=a_{1}+(5-1)d](https://tex.z-dn.net/?f=a_%7B5%7D%3Da_%7B1%7D%2B%285-1%29d)
![a_{5}=a_{1}+(4)d](https://tex.z-dn.net/?f=a_%7B5%7D%3Da_%7B1%7D%2B%284%29d)
Substituting the value we get
![a_{5}= 3+(4)-2](https://tex.z-dn.net/?f=a_%7B5%7D%3D%203%2B%284%29-2)
![a_{5}= 3-8](https://tex.z-dn.net/?f=a_%7B5%7D%3D%203-8)
![a_{5}= -5](https://tex.z-dn.net/?f=a_%7B5%7D%3D%20-5)