Sequences and Series Part 2

Multiples of 11 such that they are of 3-digit and less than 500.
121, 132, ..., 495
n=

495−121

11

+1=35
S=

35

2

(121+495)=10780
Again, multiplies of 11 which are 3-digits, less than 500 and having 1 at hundred’s place are
121, 132, ..., 198
n1=(

198−121

11

)+1=8
S1=

8

2

(121+198)=1276
The multiply of 11 which are of 3-digits, less than 500 and having 1 at ten’s place are 319, 418
∴ S2=319+418=737
The multiple of 11 which are 3-digits, less than 500 and having 1 at unit place are 231, 341, 451
∴ S3=231+341+451=1023
∴ Required sum =S−S1−S2−S3
= 7744