Question

MATHS :

Answer 1

Given five terms are: 6, 10.5, 15, 19.5, 24

To find: The $n_{th}$ term expressed in terms of n.

The first term $a_1 = 6$

Common difference d=10.5-6=4.5

The $n_{th}$ term of $a_n$ AP is given by the following expression:

$a_n=a_1+d(n-1)\\a_n=6+4.5(n-1)\\a_n=6+4.5n-4.5\\a_n=1.5+4.5n$

Let's check:

$a_1=1.5+4.5×1=6\\a_2=1.5+4.5×2=10.5\\a_3=1.5+4.5×3=15\\etc$

Answer: $a_n=1.5+4.5n$