How do you find #S_n# for the arithmetic series #a_1=-5#, d=3, n=14?

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Answer 1 · 2016-10-30T11:03:24

Sum is #203#

Sum upto #n# terms of an arithmetic series, whose first term is #a_1# and common difference is #d# is given by

#S_n=n/2(2a_1+(n-1)d)#

Hence, sum of first #14# terms of the series with first term as #-5# and #3# as common difference is

#14/2(2×(-5)+(14-1)×3)#

= #7×(-10+13×3)#

= #7×(-10+39)#

= #7×29#

= #203#