(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

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)

or, 6x - 21 = 12x - 54

or, 12x - 6x = - 21 + 54 = 33

or, 6x = 33

or, 2x = 11

∴ x = 11/2

∴2x + 23 = 2 × 11/2 + 23 = 34

8x + 2 = 8 × 11/2 + 2 = 46 and

20x - 52 = 20 × 11/2 - 52 = 110 - 52 = 58

34, 46 and 58 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.

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step-by-step explanation:

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: