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Visualize the concept of consecutive terms in an arithmetic progression. Show the numeric values 4 and 13 on the line as the first and fourth positions. Represent the terms p and q as abstract symbols in the second and third positions respectively. Immerse this line in an attractive and appealing mathematical setting, perhaps on a chalkboard or as scribbles on a notebook page. Keep a clean and clear aesthetic to provide a sense of simplicity and clarity. Please ensure that there is no text within the image.

Given that 4,p,q,13 are consecutive terms of a a.p find the value of p and q

First use this formula nth=a d(n-1)

13=4 d(4-1). 13=4 3d
13-4=3d. 3d/3=9/3
d=3
Secondly to find p and q use the formula for finding common difference( D )
Therefore d=2nd term-1st term
3=p-4. P=3 4=7
P=7
Since 3rd term=a 2d. q=a 2d. q=4 2(3)
q=4 6. q=10

Please the formula was not stated very well to get the answer as somebody who is learning mathematics it will not be clear on u get ur answers.

Show me the complete workings

Q=10

Still dont get it pls

First of all our it this way

p-4=q-p
q-p=q+13
Then collect like terms and solve simultaneously
Ur answer will be p=7, q=10

p-4 = q-p

q-p = 13-q

Now just solve for q and p

Or, note that there are two equally-spaced terms between 4 and 13. So, the difference (13-4) is divided into three equal parts. That should help.