untitled

The first quantity of the sequence is called the first term, the second quantity is called second term, the third quantity is ca ...

0DWK,;;)RUPD first term a a( 1  1 )d second term ad a( 2  1 )d third term a 2 d a( 3  1 )d forth term a 3 d a( ...

or, 2Sn n ap [number of terms of the series is n] ? ( ) 2 a p iii n Sn  Again,nth term p a(n 1 )d. Putting this value of p ...

? n 99 4950 2 99 100 u From (iv) formula, the sum of first n-terms of an arithmetic series { 2 ( 1 ) }. 2 a n d n Sn   Hence, ...

1200  1300  1400 ( 100 n 1100 ) (iii) In n-numbers of months, he deposits Tk. { 2 ( 1 ) } 2 a n d n   = Tk. { 2 1200 ( ...

The sum of the first m terms of an arithmetic series is n and the first n terms is m. Find the sum of first (m+n) terms. 1 8. ...

The sum of cubes of the first n numbers of Natural Numbers etL Sn be the sum of cubes of the first n numbers of natural numbers. ...

Geometric series If the ratio of any term and its antecedent term of any series is always equal i.e., if any term divided by its ...

Solution : The first term of the series a 2 , common ratio 2. 2 4 r ? The given series is a geometric series. We know that the n ...

0DWK,;;)RUPD Hence, in this case Sn aaa upto n. an. Activity : A employed a man from the first April for taking his ...

Exercise 13.2 1 .If a,b,c,d are cosecutive four terms of a arithmetic series, which one is correct ? (a) 2 c d b  (b) 2 b c a  ...

What is sum of ( 2 n 2 ) terms of the series 2  2  2  2 ? 1 8. If the sum of cubes of n natural numbers is 441, find th ...

Chapter Fourteen Ratio, Similarity and Symmetry For comparing two quantities, their ratios are to be considered. Again, for dete ...

Hence, the area of the triangle ABC = auh 2 1 and the area of the triangle DEF= duh 2 1 . Therefore, area of the triangle ABC : ...

DB AD BDE ADE ' ' ? (2) Again, The heights of 'ADE and 'DEC are equal. EC AE DEC ADE ' ' ? (3) But 'BDE 'DEC DEC ADE BDE ADE ' ' ...

(2) But EC AE DB AD (3) Therefore, DEC ADE BDE ADE ' ' ' ' ? 'BDE 'DEC (4) But 'BDE and 'DEC are on the same side of the common ...

Proposition : Let ABCbe a triangle and the line segment AD from vertexAdivides the side BC at D such that BD : DC = BA : AC. It ...

0DWK,;;)RUPD If the heights of the equiangular triangles ABC and DEF are AMandDN respectively, prove that AM : DN = AB : ...

Theorem 5 If two triangles are equiangular, their matching sides are proportional. Proposition : Let ABC and DEF be triangles wi ...

Proposition : Let in 'ABC and 'DEF, EF BC DF AC DE AB . It is to prove that, ‘A ‘D,‘B ‘E,‘C ‘F. Construction: Consider the match ...