Arithmetic Sequences Continued A. Determine the common difference for each arithmetic sequence, then fill in the blanks.
5, _, _, 17

The common difference is 4

5, 9, 13, 17

Step-by-step explanation:

Given

5, _, _, 17

Solving (a): The common difference

Since it is an arithmetic sequence, the common difference can be solved using:

Where

i.e. 4 terms

So:

Collect like terms

Hence, the common difference is 4

Solving (b): Complete the blanks.

To do this, we simply add 4 to each successive terms.

So: 5, 9, 13, 17

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

answer: 5100 just subtract

step-by-step explanation: