Question

MATHS :

Find an expression, in terms of n, for the nth term of the sequence 6, 10.5, 15, 19.5, 24​

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:

`</p><p>a_n=a_1+d(n-1)\\</p><p>a_n=6+4.5(n-1)\\</p><p>a_n=6+4.5n-4.5\\</p><p>a_n=1.5+4.5n </p><p>`

Let's check:

`</p><p>a_1=1.5+4.5×1=6\\</p><p>a_2=1.5+4.5×2=10.5\\</p><p>a_3=1.5+4.5×3=15\\</p><p>etc</p><p>`

Answer:
`a_n=1.5+4.5n`