Find the sum of the integers between 2 and 100 which are divisible by 3 ?
Arithmethic Series
Arithmethic Series
1 Answer
Jul 19, 2018
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#