How do you write the first five terms of the arithmetic sequence given #a_1=5/8, a_(k+1)=a_k-1/8# and find the common difference and write the nth term of the sequence as a function of n?

1 Answer
Aug 12, 2017

Answer:

Common difference is #-1/8# and #n^(th)# term is #(6-n)/8#. First five terms are #{5/8,1/2,3/8,1/4,1/8}#.

Explanation:

Common difference is the difference between a term and it's immediately preceding term. In other words as first term is #a_1# and common difference is #d#, next term is #a_1+d# and then #a_1+2d#. Observe that this way #a_n=a_1+(n-1)×d#.

Let us consider a term #a_k#, ita next term would be #a_(k+1)# and common difference is

#a_(k+1)-a_k#

but as in given case #a_(k+1)=a_k-1/8#,
#a_(k+1)-a_k=-1/8#. Hence common difference is #-1/8#.

As first term is #5/8#, we have #a_2=5/8-1/8=4/8=1/2#, #a_3=4/8-1/8=3/8#, #a_4=3/8-1/8=2/8=1/4#, #a_5=2/8-1/8=1/8#. Hence first five terms are #{5/8, 1/2, 3/8, 1/4, 1/8}#.

and #n^(th)# term is given by #a_n=5/8+(n-1)×(-1/8)#

= #5/8-n/8+1/8#

= #(6-n)/8#