# How do you write the first five terms of the arithmetic sequence given a_1=72, a_(k+1)=a_k-6 and find the common difference and write the nth term of the sequence as a function of n?

Sep 26, 2017

First five terms are $72 , 66 , 60 , 54 \mathmr{and} 48$. The $n$ th term of the sequence is ${T}_{n} = 72 - 6 \left(n - 1\right)$

#### Explanation:

${a}_{1} = 72 , {a}_{k + 1} = {a}_{k} - 6 \therefore {a}_{2} = {a}_{1} - 6 = 72 - 6 = 66$

 a_3 =a_2-6=66-6=60 ; a_4 =a_3-6=60-6=54

${a}_{5} = {a}_{4} - 6 = 54 - 6 = 48 \therefore$ First five terms are

$72 , 66 , 60 , 54 \mathmr{and} 48$. This is arithmatic progression

series of which common difference is $d = 66 - 72 = - 6$

similarly $d = 60 - 66 = - 6$ . The $n$ th term of the sequence

is ${T}_{n} = {a}_{1} + \left(n - 1\right) d \mathmr{and} {T}_{n} = 72 + \left(n - 1\right) \cdot - 6$ or

${T}_{n} = 72 - 6 \left(n - 1\right)$ , Check ${T}_{5} = 72 - 6 \left(5 - 1\right) = 48$ [Ans]