Question

(2x+23),(8x+2) and (20x-52) are three consecutive terms of an arithmetic sequence.

prove that the common difference of the sequence is 12

Answer 1

The common difference of the sequence is 12, proved.

Step-by-step explanation:

Given, (2x + 23), (8x + 2) and (20x - 52) are three consecutive terms of an arithmetic sequence.

∴ (8x + 2) · (2x + 23) = (20x - 52) - (8x + 2)

⇒ 6x - 21 = 12x - 54

⇒ 12x - 6x = - 21 + 54 = 33

⇒ 6x = 33

⇒ 2x = 11

∴ x = $\dfrac{11}{2}$

∴2x + 23 = 2 × $\dfrac{11}{2}$ + 23 = 11 + 23 = 34,

8x + 2 = 8 × $\dfrac{11}{2}$  + 2 = 44 + 2 =  46 and

20x - 52 = 20 × $\dfrac{11}{2}$ - 52 = 110 - 52 = 58

34, 46 and 46 are three consecutive terms of an arithmetic sequence.

∴ Common difference(d) = 46 - 34 = 58 - 46 = 12, it is proved.

Hence, the common difference of the sequence is 12.