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3 years ago

If a fixed number is added to each term of an arithmetic sequence, is the resulting sequence an arithmetic sequence?

Mathematics

2 answers:

Tom [10]3 years ago

7 0

Yes. But, if the number is multiplied/divided, then it would be a geometrical.

devlian [24]3 years ago

7 0

Answer: Yes, the resulting sequence is an arithmetic sequence.

Step-by-step explanation: Given that a fixed number is added to each term of an arithmetic sequence.

We are to check whether the resulting sequence is an arithmetic one or not.

Let the first term of an arithmetic sequence is a and its common difference is d.

Then, the first few terms of the sequence are given by

$a,~a+d,~a+2d,~a+3d,~~.~~.~~.$

Now, if we add a fixed number k to each term of the sequence, then the sequence will be pf the form :

$a+k,~a+d+k,~a+2d+k,~a+3d+k,~~.~~.~~.$

Here, we notice that

first term is (a + k) and

$(a+d+K)-(a+k)=(a+2d+k)-(a+d+k)=(a+3d+k)-(a+2d+k)=~~.~~.~~.~~=d.$

Therefore, the difference between the consecutive terms in the resulting sequence will also be d.

Thus, the resulting sequence is an arithmetic sequence with first term (a + k) and common difference d.

The answer is YES.

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Step-by-step explanation:

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4 years ago

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3 years ago

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4 years ago

If a fixed number is added to each term of an arithmetic​ sequence, is the resulting sequence an arithmetic​ sequence?

If a fixed number is added to each term of an arithmetic sequence, is the resulting sequence an arithmetic sequence?