How do you find the sum of the arithmetic sequence having the data given #a_1=81#, #a_n = - 13#, n = 20?

1 Answer
Apr 5, 2016

Answer:

#680#

Explanation:

The sum of a series is

#n/2["first" + "last"]#,

where #n# is the number of terms (in this case 20), #"first"# is the first term in the series and #"last"# is the last one.

Substituting in our values of #"first" = 81, "last" = -13, n = 20#

#10[81 - 13] = 680#

which is the sum of the series between #n = 1# and #n = 20#.

If you wanted to find the total sum between #n = 1# and #n = oo#, you can solve this one using mere common sense.

The series clearly has a decreasing common difference if the first is #81# and the 20th is #-13#, and so there will be in total more terms that are negative than positive, as everything after #-13# will also be negative. Therefore, adding them all together, you will approach #-oo#.