Given five terms are: 6, 10.5, 15, 19.5, 24
To find: The [tex] n_{th} [/tex] term expressed in terms of n.
The first term [tex] a_1 = 6[/tex]
Common difference d=10.5-6=4.5
The [tex] n_{th} [/tex] term of [tex] a_n[/tex] AP is given by the following expression:
[tex]
a_n=a_1+d(n-1)\\
a_n=6+4.5(n-1)\\
a_n=6+4.5n-4.5\\
a_n=1.5+4.5n
[/tex]
Let's check:
[tex]
a_1=1.5+4.5×1=6\\
a_2=1.5+4.5×2=10.5\\
a_3=1.5+4.5×3=15\\
etc
[/tex]
Answer: [tex] a_n=1.5+4.5n[/tex]
