How do you find the sum of the first 40 terms of the series #50+42+34+26+18+...#?

1 Answer
Jul 21, 2016

Sum of first 40 terms of the given series is #-4240#

Explanation:

The series #50+42+34+26+18+...........# is arithmetic series whose fist term is #a# and difference between a term and its immediate preceding term is #-8#.

In an arithmetic series, whose first term is #a# and difference between a term and its immediate preceding term is #d#

#n^(th)# term is #a+(n-1)d# and

sum of first #n# terms is #n/2(2a+(n-1)d)#

Hence sum of first 40 terms of the given series is

#40/2xx(2xx50+(40-1)xx(-8))#

= #20xx(100+39xx(-8))=20xx(100-312)#

= #20xx(-212)=-4240#