Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1 = 3/5, d= -1/3?

1 Answer
Sep 19, 2015

Answer:

#a_n = a_1 + (n-1)d#
#A.P(9/15,4/15,-1/15,-6/15,-11/15)#

Explanation:

The concept of an arithmetic sequence is that, from the first term, every term after has a common difference between, so

#a_n - a_(n-1) = a_(n-1) - a_(n-2) = ... = a_3 - a_2 = a_2 - a_1 = d#

Which means, that we can rewrite #a_2# as #a_1 + d#, and we can also rewrite #a_3# as #a_2+d# or #a_1 + 2d# and so on, until we start seeing a pattern. #a_n = a_1 + (n-1)d#, because we can put #a_(n-1)# in terms of #a_(n-2)# and that in terms of #a_(n-3)# and so on down to #a_1#, doing a total of #(n-1)# rewrites.

As for the terms, it's just a matter of evaluating in your matter of choice.
#a_1 = 3/5 = 9/15#
#a_2 = 3/5 - 1/3 = 9/15 - 5/15 = 4/15#
#a_3 = 3/5 -2/3 = 9/15 - 10/15 = -1/15#
#a_4 = 3/5 - 3/3 = 9/15 - 15/15 = -6/15#
#a_5 = 3/5 - 4/3 = 9/15 - 20/15 = -11/15#