Question

How do you write the first five terms of the arithmetic sequence given `a_1=-.375, a_(k+1)=a_k+0.25` and find the common difference and write the nth term of the sequence as a function of n?

Answer 1

First `5` terms of arithmatic sequence is
`{-0.375, -0.125 ,0.125 , 0.375, 0.625} and n` th term of the arithmatic sequence is `a_n= -0.375+ (n-1)0.25`

Explanation:

`a_1= -0.375 , a_(k+1)= a_k+0.25`. Common difference

is `d= a_(k+1)-a_k ; a_(k+1)-a_k= 0.25 :. d= 0.25`

First term is `a_1= -0.375`

Second term is `a_2=a_1+d= -0.375+0.25= -0.125`

Third term is `a_3=a_1+2d= -0.375+2*0.25= 0.125`

Fourth term is `a_4=a_1+3d=- 0.375+3*0.25= 0.375`

Fifth term is `a_5=a_1+4d= -0.375+4*0.25= 0.625`

First `5` terms of arithmatic sequence is

`{-0.375, -0.125 ,0.125 , 0.375, 0.625}`

`n` th term of arithmatic sequence is `a_n=a_1+(n-1)d` or

`a_n= -0.375+ (n-1)0.25` [Ans]