Question

Find sum of all two digit numbers when divided by 7 gives remainder 1

Answer 1

the lowest two digit number=10

highest two digit number is=99

now ...the lowest two digit number leaving remainder 1 when divide by 7 is =7×2+1=15

and the highest of the same is =7×14+1=99

now ....the series is....

15,22,29,36,.....,99

let 99 is the nth term.....

therefore....,

$99 = 15 + (n - 1)7 \\ = > 99 - 15 + 7 = 7n \\ = > n = \frac{91}{7} \\ = > n = 13$

therefore...the sum of 13th terms is ....

$s(13) = \frac{13(15 + 99)}{2} =741$

Answer 2

Question :-

Find sum of all two digit numbers when divided by 7 gives remainder 1

Answer :-

the lowest two digit number=10

highest two digit number is=99

now ...the lowest two digit number leaving remainder 1 when divide by 7 is =7×2+1=15

and the highest of the same is =7×14+1=99

now ..the series is..

15,22,29,36,.,99

let 99 is the nth term.

therefore ,

=> 99 = 15 + (n - 1 ) 7

=> 99 - 15 + 7 = 7n

=> n = 91/7

=> n=13

therefore...the sum of 13th terms is

s(13) = 13(15+99)/2 = 741

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↪️ llMichhChocoll