If each term of an arithmetic sequence is multiplied by a fixed number, will the resulting sequence always be an arithmetic sequence?

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.  

where

is the nth term of the sequence.

Now, when  each term of an arithmetic sequence is multiplied by a fixed number let a'.

Let is the nth term of the new sequence.

Then we have:

and so on

Also,

for each n.

Hence, the sequence will again be an arithmetic sequence.

          ( Since, the sequence again vary by a fixed constant )

b.-4 units

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