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Math Assignment Class X Ch-5 | Arithmetic Progression

MATHEMATICS ASSIGNMENT   [CHAPTER 5]

Extra questions of chapter 5 class 10 Arithmetic Progression with answer and  hints to the difficult questions. Important and useful math assignment for the students of class 10

Basic points of  Arithmetic Progression 

Assignment on Arithmetic Progression

Question 1Which term of the AP:-  5, 9, 13, 17..........is 81.   
Ans [20th term]
Question 2: Which term of the following APs are equal    
a) 13, 19, 25...........     b) 69, 68, 67 ..........
Ans  [9th term]
Question 3: How many terms of the AP: 3, 5, 7.......must be taken so that   Sn =   120.
Ans [10 terms] 
Question 4: Find the 10th term from the end of the AP :-  4, 9, 14..........254 
Ans [209]
Question 5: If 7th term  of an AP is  -4 and 13 term is -16 find the AP
Ans  [8, 6, 4, 2, 0 .........]
Question 6: Find k for which 8k + 4, 6k - 2 and 2k + 7 are in AP.  
Ans [k = 15/2] 
Question 7: Find a So that  3a + 2,  3a - 1,  5a + 4  are in AP.    Ans  [-4]  
Question 8: If a = 7, a60 = 125, find a32     Ans  [69]
Question 9: Which term of the AP: 5, 13, 21, .... is 181.       Ans [23rd ] 
Question 10: Find AP whose 3rd term is 16 and difference of 5th term from 7th term is 12.

Ans [4, 10, 16, 22 ...] 

Question 11:Which term of the AP: 3, 15, 27, 39........will be 120 more than its 64th term 

Ans [74th]

Question 12: Which term of the AP: 3, 15, 27, 39........will be 132 more than its 60th term

Ans [ 71st term]

Question 13: Which term of the AP : 8, 14, 20, 26........will be 72 more than its 41st term.

Ans  [53rd ]  

Question 14: The 3rd  term of an AP is 3 and its 11th term is -21. Find its first term and c.d. 

Ans [a = 9, d = - 3] 

Question 15: The 7th term of an AP is 32 and its 13th term is 62. Find the AP                         

Ans [2, 7, 12......]

Question 16: If tn = 4n - 5. Then find the sum of first 25 terms.      Ans [1175]
Question 17: If tn = 2 - 3n. Then find the sum of first 25 terms.     Ans [-925]
Question 18: Sn = 2n2 + 5n,   find  its nth term.       Ans  [4n + 3]
Question 19: In an AP, the sum of its first n terms is 3n2 + n. Find its 22nd term.                   

 Ans [130]

Question 20: The sum of the first n terms of an AP. Is  3n2 + 6n. Find the nth term of this A.P.    

Ans [6n + 3]

Question 21: If Sn  = 5n+ 3n. Find its nth term.      Ans [10n - 2]

Question 22: If Sn  = 4n- 3n.. Find its nth term.     Ans [8n-7]

Question 23: The 6th term of an AP is -10 and 10th term is -26. Find the 15th term of the AP.

Question 24 : Find the sum of all two digit no. Which are divisible by 4. 

Ans [1188]

Question 25: Find the no. Of terms of an AP: 54, 51, 48....... so that their sum is  513.          

Ans [18 or 19]

Question 26: Find the sum of all natural no. Between 100 & 300 which are divisible by 6        

Ans [6534]

Question 27: Find the sum of all natural no. Between 200 & 300 which are divisible by 4        

Ans [6000]

Question 28: The 5th term of  an AP is zero. Show that its 33rd term is 4 times its 12th term.

Question 29: If 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.

Question 30: If the seventh term of an AP is 1/9 and its 9th term is 1/7, find its 63rd term.     

 Ans[1] 

Question 31: Find the 9th term from the end of the AP:   5, 9, 13, …….185.                      

Ans [153]

Question 32: Find the sum of 11 terms of an AP whose middle term is 30.                              

Ans [330]

Question 33: Find the sum of all integers between 50 & 500 which are divisible by 7             

Ans [17696]

Question 34: The sum of first 15 terms of an AP is 105 and the sum of next 15 terms is 780. Find first   three terms of an AP.    

Ans [-14, -11, -8]

Question 35: Find the common difference of an AP whose 1st term is 100 and the sum of whose first 6 terms  is 5 times  the sum of next 6 terms.  

Ans [-10]

Question 36: Find the no. Of  natural no. Which lie between 101 and 304 and are divisible by  3 or  5. Also find their sum. 

 Ans [94 terms , sum= 19035]

Question 37: The ratio of the 7th to the 3rd term of an AP is 12 : 5 Find t13  :  t14   

 Ans [90 : 97]

Question 38: Find the sum of all 3 digit no. Which leaves remainder 3 when divided by 5 

Ans [99090]

Question 39: The sum of 4 terms in an AP is 42. If product of extreme terms is 90. Find no.  

Ans [6, 9, 12, 15]

Question 40: Sum of 3 terms of an AP is  21 and their product is 231. Find the numbers.        

Ans [3, 7, 11]

Question 41:Find 4 numbers in AP whose sum is 20 and sum of whose square is  120.            

Ans [2, 4, 6, 8]

Question 42: If angles of a quadrilateral are in AP whose c. d. Is 10. Find all the angles.    

Ans [75, 85, 95, 105]

Question 43: The first and last term of an AP is a  & l show that sum of the nth term from the beginning and nth term from the last is a + l.

Question 44: Find the sum of first hundred even natural number which are divisible by 5.           

Ans [50500]

Question 45: Which term of the AP: 5, 9, 13, 17.....is 81 also find their sum.                          

Ans [20th , 860]

Question 46: If in an AP sum of first 10 terms is -80 and the sum of its next 10 terms is -280. Then find AP.                                                                                                                               

 Ans [1, -1, -3, -5]

Question 47: Find the sum of all multiple of 8 lying between  201 and 950.

Question 48: If 21, a,  b, -3 are in AP. Then find the value of  (a + b)                                    

Ans[18]

Question 49: The angles of a triangle are in AP. The greatest angle is twice  the least. Find the angles of the triangle. 

Ans[40o, 60o and 80o]

Question 50: If 7 time the 7th term of an Ap is equal to the 11 times  the 11th term. Show that the 18th term of the AP is zero.

Question 51: If m times the mth term of an AP is equal to the n times of the nth term then show  that  its    (m + n)th is zero.

Question 52: The first term of an A.P. is 5, the last term is 45 and the sum of all the terms is 400. Find the number of terms and the common difference of the A.P.

Answer: n=16, d=8/3

Question 53: The ratio of the 10th term to its 30th term of an A.P. is 1:3 and the sum of its first 6 terms is 42. Find the first term and the common difference of A.P.

Answer: a = 2 and d = 2

Question 54: The sum of first and 8th terms of an A.P. is 32 and their product is 60. Find the first term and common difference of the A.P. Hence also find the sum of its first 20 terms.

Answer a = 2 or 30, d = 4 or -4, Sn = 800 or -160

Question 55: An A.P. of 40 terms, the sum of first 9 terms is 153 and the sum of last 6 terms is 687. Determine the first term and common difference of A.P. Also, find the sum of all the terms of the A.P.

Answer: a =5, d = 3, S40 = 2540

Question 56: In an A.P., the sum of three consecutive terms is 24 and the sum of their aquares is 194. Find the numbers.

Answer: Numbers are 7, 8, 9 or 9, 8, 7


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