Answer:
x = -2
Step-by-step explanation:
An arithmetic sequence is one where the difference between any two consecutive terms in the sequence is constant.
For any arithmetic sequence the general formula is as follow
[tex]a_{n} = a_{1} + (n - 1)d[/tex]
where
[tex]a_{n}[/tex] is the nth arithmetic value
[tex]a_{1}[/tex] is the initial arithmetic value
[tex]n[/tex] is the nth term
[tex]d[/tex] is the difference is consecutive arithmetic values
To find the value of [tex]x[/tex] we form a number of simultaneous equations
[tex]a_{1} = 3 + x\\ a_{2} = (3 + x) + 1 d\\ a_{3} = (3 + x) + 2 d[/tex]
from the given information we also know that
[tex]a_{2} = 9 + 3 x\\ a_{3} = 13 + 4x[/tex]
Solving these equations simultaneous we find the value of x to be
[tex]x = -2[/tex]
