In A.P.
a1 = initial term of arithmetic progression
d = common difference
nth term of A.P.
an = a1 + ( n - 1 ) d
In this case a1 = x , a2 = 3 x + 1 , a3 = 7 x - 4 so:
a1 = x
a2 = a1 + ( 2 - 1 ) d
a2 = a1 + d
3 x + 1 = x + d
a3 = a1 + ( 3 - 1 ) d
a3 = a1 + 2 d
7 x - 4 = x + 2 d
Now you must solve system:
3 x + 1 = x + d
7 x - 4 = x + 2 d
Ttry it.
The solutions are:
x = 3 , d = 7
a1 = x = 3
an = a1 + ( n - 1 ) d
a10 = a1 + ( 10 - 1 ) d
a10 = a1 + 9 d
a10 = 3 + 9 β 7 = 3 + 63 = 66
Your A.P.
3 , 10 , 17 , 24 , 31 , 38 , 45 , 52 , 59 , 66 ...
Proof:
a1 = x = 3
a2 = 3 x + 1
10 = 3 β 3 + 1 = 9 + 1 = 10
a3 = 7 x - 4
17 = 7 β 3 - 4 = 21 - 4 = 17