Answer to Question #284344 in Geometry for Aparna

Question

11. Find 8th term of the sequence 1,5,9.......

12. If central angle of an arc is 200º,then find the angle made by the arc on the

alternate arc?

13. Prove that a rectangle is always cyclic

14. If algebraic form of an arithmetic sequence is 3-5n,find first term and common

difference

15. Find number of multiples of 11 in between 100 a nd 200

Answer 1

11. It is the arithmetic sequence, so a_n=a₁+d*(n-1).

a₁=1, d=a₂-a₁=5-1=4.

a₈=a₁+7*d=1+7*4=29.

Answer: 8th term of the sequence is 29.

12. The angle made by an arc of a circle on

the alternate arc is half the angle made at

the centre. So if central angle is 200°, then answer will be 200°*1/2=100°.

13. Any rectangle have all it's angles 90° each. The quadrilateral is cyclic, if the opposite angles that lie on the same diagonal add 180°. In any rectangle sum of opposite angles will be 90°+90°=180°. So any rectangle is cyclic quadrilateral.

14. First term: a₁=3-5*1=-2;

Second term: a₂=3-5*2=-7;

Common difference: d=a₂-a₁=-7-(-2)=-5.

Answer: first term is -2 and common difference is -5.

15. 100 < 11n < 200;

100/11 < n < 200/11;

9 1/11 < n < 18 2/11;

n=10.. 18 (n is a whole number from 10 to 18). From 10 to 18 is total 9 whole numbers.

Answer: 9 multiples of 11 is in between 100 and 200.