How do you find the sum of the first 32 terms of the series #34+31+28+25+22...#?

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Answer 1 · 2017-01-09T17:43:13

The sum of the first #32# terms of the series is #-400#

As the terms in the series #34+31+28+25+22......# are constantly coming down starting from first term #34# by #3#,

this is an arithmetic series staring from #a=34# and #d=-3#

The sum of such a series up to #n# terms is

#n/2(2a+(n-1)d)#

Hence, the sum of the first #32# terms of the series is

#32/2xx(2xx34+(32-1)xx(-3))#

= #16xx(68-31xx3)#

= #16xx(68-93)#

= #16xx(-25)#

= #-400#