if the corresponding terms of two arithmetic sequences are a

if the corresponding terms of two arithmetic sequences are added, is the resulting sequence arithmetic?

Solution

If the corresponding terms of two arithmetic sequences are added,then resulting sequence is also a arithmetic sequence.

Because arithmatic sequence is the sequence where one number is obtained from it\'s previous number by adding any number.Addition of this type of two sequences reults in the arithmatic sequence.

Let us take an example:

Arithmatic sequence 1: 5,9,13,17,21,25 (number is 4 greaterthan the previous number)

Arithmatic sequence 2: 3,1,-1,-3,-5.-7 (number is 2 lessthan the previous number)

Addition of these two sequences : 5+3, 9+1, 13+(-1), 17+(-3), 21+(-5), 25+(-7)

  5+3, 9+1, 13-1, 17-3, 21-5, 25-7

8,10, 12,14,16,18

Resulting sequence is 8,10, 12,14,16,18 (number is 2 greaterthan the previous number) which is a arithmatic sequence.

Therefore,if the corresponding terms of two arithmetic sequences are added, then resulting sequence will be arithmetic sequence.