Find the sum of the integers between 2 and 100 which are divisible by 3 ?

Arithmethic Series

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1 Answer
Jim G.
Jul 19, 2018

#1683#

Explanation:

#"the multiples of 3 between 2 and 100 are"#

#3,6,9, ...... ,99#

#"this is an arithmetic sequence with"#

#a_1=3" and "d=9-6=6-3=3#

#"the number of terms "n=99/3=33#

#•color(white)(x)S_n=n/2[2a+(n-1)d]#

#S_(33)=33/2[(2xx3)+(32xx3)]#

#color(white)(S_(33))=33/2(6+96)#

#color(white)(S_(33))=33/2xx102=33xx51=1683#

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