Find the sum of the arithmetic sequence having the data given a 1 = 81 , a n = - 13 , n = 20

Question

Find the sum of the arithmetic sequence having the data given             a      1        =    81  ,             a      n        =    -    13  , n = 20

Geovanni Shelton · Accepted Answer

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=2010[81−13]=680which 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    =    ∞  , 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       -    ∞

Find the sum of the arithmetic sequence having the data given a_1=81, a_n=−13, n = 20

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