Question

1. a) Which is the first number above 200 which leaves a remainder 3 on division by 7?
b) How many such numbers are there between 200 and 400?
c) Find the sum of these numbers?​

Answer 1

Step-by-step explanation:

If any number x on division by 7 given remainder 3 then we can write

x=7x+3

x lies between 200 and 400

so if x=200

then

200=7x+3

x=(200–3)/7=197/7 =28.14

Thus first no=(28+1)*7+3=29*7+3=203+3=206

Thus no are 206,213,220,………..up to 399

Let the numbers are n ,

This is an AP with a=206 d=7 and l=399

then 399=206+(n-1)*7

n-1=(399–206)/7 = 193/7=27.57

as n is a natural number so on neglecting the decimal part

n-1=27

thus n=28

hence such 28 numbers are there between 200 and 400

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Answer 2

Answer:

Step-by-step explanation:

a) The first number above 200 which leaves remainder 3 on division by 7 is 206.

b) n=28

c) 8414