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?

1 Answer
Sep 26, 2017

First five terms are 72 , 66 ,60 , 54 and 48 . The n th term of the sequence is T_n= 72-6(n-1)

Explanation:

a_1=72, a_(k+1)=a_k-6 :. 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 :. First five terms are

72 , 66 ,60 , 54 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 +(n-1) d or T_n= 72 + (n-1)* -6 or

T_n= 72-6(n-1) , Check T_5 = 72 -6(5-1) =48 [Ans]