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?

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Answer 1 · 2017-09-26T11:36:20

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

$a_1=72, a_(k+1)=a_k-6 :. a_2 =a_1-6=72-6=66$

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

$a_5 =a_4-6=54-6=48 :.$ 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]

How do you write the first five terms of the arithmetic sequence given a_1=72, a_(k+1)=a_k-6a_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?