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?

1 Answer
Feb 22, 2018

Answer:

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]