Answer:
[tex]-10,-12,-14,-16,-18,-20,-22,-24,-26,-28,...[/tex]
Step-by-step explanation:
we know that
In an Arithmetic Sequence the difference between one term and the next is a constant, called the common difference
The formula for an Arithmetic Sequence is equal to
[tex]a_n=a_1+(n-1)d[/tex]
where
d is the common difference
n is the number of terms
a_1 is the first term of the sequence
In this problem we have
[tex]a_1=-10\\d=-2[/tex]
substitute
[tex]a_n=-10+(n-1)(-2)[/tex]
[tex]a_n=-10-2n+2[/tex]
[tex]a_n=-2n-8[/tex]
so
Find the first ten terms
[tex]a_1=-10[/tex]
For n=2 ----> [tex]a_2=-2(2)-8=-12[/tex]
For n=3 ----> [tex]a_3=-2(3)-8=-14[/tex]
For n=4 ----> [tex]a_4=-2(4)-8=-16[/tex]
For n=5 ----> [tex]a_5=-2(5)-8=-18[/tex]
For n=6 ----> [tex]a_6=-2(6)-8=-20[/tex]
For n=7 ----> [tex]a_7=-2(7)-8=-22[/tex]
For n=8 ----> [tex]a_8=-2(8)-8=-24[/tex]
For n=9 ----> [tex]a_9=-2(9)-8=-26[/tex]
For n=10 ----> [tex]a_1_0=-2(10)-8=-28[/tex]
The sequence is
[tex]-10,-12,-14,-16,-18,-20,-22,-24,-26,-28,...[/tex]
