How do you find the formula for #a_n# for the arithmetic sequence #4, 3/2, -1, -7/2,...#?

1 Answer
Feb 11, 2017

Answer:

If the initial term is #a_0 =4# then #a_n=4-5/2n#
If the initial term is #a_1=4# then #a_n=4-(5 * (n-1))#

Explanation:

This appears to be an arithmetic sequence (and the question was asked under the heading Arithmetic Sequences)
Checking the difference between successive terms we see that
#color(white)("XXX")a_(i+1)=a_i - 5/2#
That is the initial value is reduced by a further #5/2# for each successive term.

When I learned this stuff (many years ago), the initial term was denoted #a_0#.
It seems that #a_1# is now a more common designation for that first term (at least that is what I think I am seeing on this site)