Question

Consider the arithmetic sequence 10, 8, 6, 4, ....

What is an expression in terms of n for the nth number in the sequence?

Answer 1

Expression in
`n^(th)` term is
`T_n =2(6-n)`

Explanation:

Arithmetic sequence 10,8,6,4,.....

first term a = 10

second term = 8

number of terms = n

common difference d = Second term - First term =
`8-10 \ =\ -2`

Now by using Arithmetic Progression Formula which states

`T_n = a+(n-1)d`

Substituting given values in the above expression we get

`T_n= 10+((n-1)*-2})= 10-2n+2= 12-2n= 2(6-n)`