Question

Consider all positive two digit number each of when divided by 7 leaves a remainder 3 what is their sum

Answer 1

The numbers can be written in the form..

7n+3

the first 2 digit Number is 10 when n=1

the last 2 digit Number is 94 when n=13

so their sum from n=1to 13

£(7n+3)

=7n(n+1)/2 +3n

=7×13×(13+1)/2 +3×13

=49×13+39

=520+39

=559

Answer 2

Hello!

Sₙ = 7n + 3

✓ n = 1 :

7 ( 1 ) + 3 = 7 + 3 = 10

✓ n = 2 :

7 ( 2 ) + 3 = 14 + 3 = 17

Then,

7n (n + 1) / 2 + 3n

⇒ 7(13) (13 + 1) / 2 + 3(13)

⇒ 49 × 13 / 39

⇒ 520 + 39 ⇒ 559

Cheers!