Question

a). What is the common difference of the arithmetic sequence x-1, x , x+1, .....?
b). If x-1 is an even number, which is the next even number?
c) prove that the product of two consecutive even numbers added to 1 gives a perfect square.

Answer 1

a. -1 is the common difference

b. 2(x-1) will be the next even number

c. let 2 and 4

2×4 = 8 + 1 = 9 = 3^2

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Answer 2

Answer:

1. common difference of the AP is 3rd term - 2nd term so x+1 - x =1ans
2. x-1 +2 is the next even number =x+1 answer
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