Question

find the value of p so that p+5, 4p+3, and 8p-2 will from successive terms of an arithmetic sequence, then find the three successive terms.

Answer 1

p+5, 4p+3, 8p-2
If they are in arithmetic sequence, then have a common difference or
(4p + 3) - (p + 5) = (8p - 2) - (4p + 3)

Solving for p,
4p + 3 - p - 5 = 8p - 2 - 4p - 3
3p - 2 = 4p - 5
3p - 4p = -5 + 2
-p = -3
p = 3

To get the value of each term just substitute the value of p in each term.
hope this helps~ `u`

Answer 2

as we formula:2b=a+c
2(4p+3)=p+5+8p-2
8p+6=9p+3
-p=-3
p=3
1)8
2)15
3)22