Answer:
yes correct, also when you are adding or subtracting
Step-by-step explanation:
Yes, the resulting sequence will always be an arithmetic sequence.
We know that any arithmetic sequence is a sequence in which each term of the sequence is increased by a fixed constant as compared to the preceding term of the sequence.
This fixed constant is known as common difference,
i.e. [tex]d=a_n-a_{n-1}[/tex]
where
[tex]a_n[/tex] is the nth term of the sequence.
Now, when each term of an arithmetic sequence is multiplied by a fixed number let a'.
Let [tex]a_n'[/tex] is the nth term of the new sequence.
Then we have:
[tex]a_1'=a'a_1[/tex]
[tex]a_2'=a'a_2[/tex]
[tex]a_3'=a'a_3[/tex]
and so on
Also,
[tex]a_{n}'-a_{n-1}'=a'a_n-a'a_{n-1}\\\\a_{n}'-a_{n-1}'=a'(a_n-a_{n-1})\\\\a_{n}'-a_{n-1}'=a'd[/tex]
for each n.
Hence, the sequence will again be an arithmetic sequence.
( Since, the sequence again vary by a fixed constant )
