Write down the sequence of natural numbers leaving remainder 1 on division by 3 and the sequence of natural numbers leaving remainder 2 on division by 3. Arithmetic sequence

 3)Write down the sequence of natural numbers leaving remainder 1 on division by 3 and the sequence of natural numbers leaving remainder 2 on division by 3.

Ans:



 The numbers that leave 1 as reminder when devided by 3 are 1,4,10..

(Sequence each with difference of 3 and starting from 1)

 The no. That leave 2 as reminder when divided by 3 are 

2,5,8,11,14,... (sequence each with difference of 3 and starting from 2)


.

Comments

Post a Comment

Popular posts from this blog

If circles are drawn with each side of a triangle of sides 5 centimetres, 12 centimetres and 13 centimetres, as diameters, then with respect to each circle, where would be the third vertex?. Circles

Image
 3)If circles are drawn with each side of a triangle of sides 5 centimetres, 12 centimetres and 13 centimetres, as diameters, then with respect to each circle, where would be the third vertex? Answer: Let, ABC be a triangle with sides AB= 12cm BC = 5cm and AC = 13cm Case 1:   Let us draw a circle considering AB = 12cm as a diameter Then, point C lies outside the circle. Case 2:   Let us draw a circle considering BC = 5cm as a diameter Then point A lies outside the circle  Case 3: Let us draw a circle considering AC = 13cm as a diameter Then. Point B lies outside the circle 
Read more

In the picture, a circle is drawn with a line as diameter and a smaller circle with half the line as to diameter. Prove that any chord of the larger circle through the point where the circles meet is bisected by the small circle. Circles

Image
4) In the picture, a circle is drawn with a line as diameter and a smaller circle with half the line as to diameter. Prove that any chord of the larger circle through the point where the circles meet is bisected by the small circle. Answer : ∠ A is common to both the triangles. AO � 1  = BO 1  (the radii of the big circle) ∠ ACO 1   =   ∠ ADB = 90° Hence, in ΔACO 1 ∼   ΔADB, ⇒   Since, the ratio is always equal, we can say that   any chord of the larger circle through the point where the circles meet is bisected by the small circle.
Read more