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

Answer:

Expression in $n^{th}$ term is $T_n =2(6-n)$

Step-by-step 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

$T_n= 10+((n-1)\times-2})= 10-2n+2= 12-2n= 2(6-n)$