Consider the arithmetic sequence x+2, 18-x, 14+x,...

Question

a) Find the value of x.
b) Find the general term of the arithmetic sequence.

Answer 1

in general an = a1 + (n-1)d
d = (18-x)-(x+2) = (14+x)-(18-x)
d = 16 -2x = -4 +2x
so
4 x = 20 and x = 5

then d = -4 + 2x = 6
so
an = a1 + (n-1)6
if the first term is x+2 = 7
then the sequence is
an = 7+(n-1)6

Answer 2

2,10,18,26

Answer 3

a1= 2
d=8
n=4

a5=2+(5-1)8
a5=2+32
a5=34