VERY SHORT ANSWER TYPE QUESTIONS (1 MARK)

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1 VERY SHORT ANSWER TYPE QUESTIONS ( MARK). If th term of a A.P. is 6 7 the write its 50 th term.. If S = +, the write a. Which term of the sequece,, 0, 7,... is 6? 4. If i a A.P. 7 th term is 9 ad 9 th term is 7, the fid 6 th term. 5. If sum of first terms of a A.P is + 7, write its th term. 6. Which term of the G.P.,,,,... is? If i a G.P., a + a5 = 90 ad if r = fid the first term of the G.P. 8. I G.P., 4,..., 8, fid the 4 th term from the ed. 9. If the product of cosecutive terms of G.P. is 7, fid the middle term 0. Fid the sum of first 8 terms of the G.P. 0,5, 5,.... Fid the value of 5 / 5 /4 5 /8... upto ifiity.. Write the value of 0.. The first term of a G.P. is ad sum to ifiity is 6, fid commo ratio. 4. Write the th term of the series, Fid the umber of terms i the A.P. 7, 0,,...,. 6. I a A.P., 8,, 4,... fid S S 7. Fid the umber of squares that ca be formed o chess board? 8. Fid the sum of give terms:- Page

2 (a) (b) (c) (d) (a) If a, b, c are i A.P. the show that b = a+c. (b) If a, b, c are i G.P. the show that b a.. c 0. If a, b, c are i G.P. the show that i G.P. a b, ab bc, b c are also SHORT ANSWER TYPE QUESTIONS (4 MARKS). Fid the least value of for which > Fid the sum of the series (+ x) + ( + x + x ) + ( + x + x + x ) Write the first egative term of the sequece 0, 9,8,7, Determie the umber of terms i A.P., 7,, Also, fid its th term from the ed. 5. How may umbers are there betwee 00 ad 500, which leave remaider 7 whe divided by Fid the sum of all the atural umbers betwee ad 00 which are either divisible by or by Fid the sum of the sequece, 5 0,,,,, 6 8. If i a A.P a 5 a fid a 7 a Page

3 9. I a A.P. sum of first 4 terms is 56 ad the sum of last 4 terms is. If the first term is the fid the umber of terms. 0. Solve: x = 48. The ratio of the sum of terms of two A.P.'s is (7 ): ( + ), fid the ratio of their 0 th terms.. If the I st, d ad last terms of a A.P are a, b ad c respectively, the fid the sum of all terms of the A.P. b c a c a a a b c. If are i A.P. the show that,, a b c a b c are also i A.P. [Hit. : Add to each term] abc 4. The product of first three terms of a G.P. is 000. If 6 is added to its secod term ad 7 is added to its third term, the terms become i A.P. Fid the G.P. 5. If the cotiued product of three umbers i G.P. is 6 ad the sum of their products i pairs is 56, fid the umbers. 6. Fid the sum to ifiity of the series: If A = + r a + r a +... up to ifiity, the express r i terms of a & A. 8. Fid the sum of first terms of the series a a b b 9. If x a... ; y b... ad r r r r c c z c... 4 r r prove that xy ab. z c Page

4 40. The sum of first three terms of a G.P. is 5 ad sum of ext three terms is 0. Fid the sum of first terms. 4. Prove that [Hit: 0.0 = Now use ifiite G.P.] 4. If log, log( ) ad log ( +) are i A.P. Show that 4. If a, b, c are i G.P. that the followig are also i G.P. (i) (ii) a, b, c a, b, c (iii) a, b, c are i G.P. 44. If a, b, c are i A.P. that the followig are also i A.P: (i) (ii) (iii),, bc ca ab b + c, c + a, a + b 45. If the umbers,, a b c b c a c a b,, b c c a a b 46. Show that: are i A.P. log 5 log a, b, c are give to be i A.P., show that are i A.P Page

5 LONG ANSWER TYPE QUESTIONS (6 MARKS) 47. Prove that the sum of umbers betwee a ad b such that the ( a b) resultig series becomes A.P. is 48. A square is draw by joiig the mid poits of the sides of a square. A third square is draw iside the secod square i the same way ad the process is cotiued idefiitely. If the side of the first square is 5 cm, the fid the sum of the areas of all the squares so formed. 49. If a, b, c are i G.P., the prove that a b b c b [Hit : Put b = ar, c = ar ] 50. Fid two positive umbers whose differece is ad whose arithmetic mea exceeds the geometric mea by. 5. If a is A.M. of b ad c ad c, G, G, b are i G.P. the prove that G G abc 5. Fid the sum of the series, upto terms. 5. Evaluate 0 r r. 54. The sum of a ifiite G.P. is 57 ad the sum of the cubes of its term is 9747, fid the G.P. Page

6 () (0) () (0)... 0() k.(0). the fid 55. If the value of k such that k N. 56. Fid the sum of first terms of the series terms. 57. Three positive umbers form a icreasig G.P. If the middle term i the G.P. is doubled, the ew umbers are i A.P. the fid the commo ratio of the G.P. 58. Show that if the positive umber a, b, c are i A.P. so are the umbers,, are i A.P. a c c a a b Fid the sum of the series: a, a, a,... a a 0i N are i A.P. where 60. If i. the show that... a a a a a a a a a a 4 6. If the sum of first terms of a A.P. is c. the prove that the c 4 sum of squares of these terms is. 6. Let p ad q be the roots of the equatio x x A 0 ad let r ad s be the roots of the equatio x 8x B 0 if p< q< r< s are i A.P. the prove that A= ad B= If S, S, S... S are the sums of ifiite geometric series whose first terms are,,, ad whose commo ratios are,,... 4 respectively, the show that the value of S S S... S 4 6 Page

7 4 A ad B Fid at least odd atural umber o, so that B A o. 64. Let th th 65. If p, q ad r th A. terms of a A.P. ad G.P. are equal ad are x, y yz zx x y ad z respectively, the prove that x. y. z ANSWERS th th ( 6)( 0) (a) 55 (b) 55 (c) 855 (d) 555 Page

8 x ( x ). = 7. x ( x). 4. 0, :7. ( b c a)( a c) ( b a) 4. 5, 0, 0,...; or 0, 0, 5, 5. 8, 6, ; or, 6, A A a cm² 50. 6, 4 5. ( ) (48 6 4) ,,, k = r Page

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