Question

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?

Answer 1

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]