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 1: Which term of the AP:-  5, 9, 13, 17..........is 81.   

Ans [20^th term]

Question 2: Which term of the following APs are equal    

a) 13, 19, 25...........     b) 69, 68, 67 ..........

Ans  [9^th 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 10^th term from the end of the AP :-  4, 9, 14..........254 

Ans [209]

Question 5: If 7^th term  of an AP is  -4 and 13 term is -16 find the AP

Ans  [8, 6, 4, 2, 0 .........]

Question 6: 

(a) Find k for which 8k + 4, 6k - 2 and 2k + 7 are in AP.  

Ans [k = 15/2] 

(b) Find a So that  3a + 2,  3a - 1,  5a + 4  are in AP.    

Ans  [-4]  

Question 7: If a = 7, a₆₀ = 125, find a₃₂     Ans  [69]

Question 8: Which term of the AP: 5, 13, 21, .... is 181.   Ans [23^rd ] 

Question 9: Find AP whose 3^rd term is 16 and difference of 5^th term from 7^th term is 12.

Ans [4, 10, 16, 22 ...] 

Question 10:

(a) Which term of the AP: 3, 15, 27, 39........will be 120 more than its 64^th term 

Ans [74^th]

(b) Which term of the AP: 3, 15, 27, 39........will be 132 more than its 60^th term

Ans [ 71^st term]

(c) Which term of the AP : 8, 14, 20, 26........will be 72 more than its 41^st term.

Ans  [53^rd ]  

Question 11: If 21, a,  b, -3 are in AP. Then find the value of  (a + b)     Ans[18]

Question 12: If angles of a quadrilateral are in AP whose c. d. Is 10. Find all the angles.    

Ans [75, 85, 95, 105]

Question 13: The 3^rd  term of an AP is 3 and its 11^th term is -21. Find its first term and c.d. 

Ans [a = 9, d = - 3] 

Question 14: The 7^th term of an AP is 32 and its 13^th term is 62. Find the AP                         

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

Question 15: 

(a) If tn = 4n - 5. Then find the sum of first 25 terms.      Ans [1175]

(b) If tn = 2 - 3n. Then find the sum of first 25 terms.     Ans [-925]

Question 16: 

(a) In an AP if Sn = 2n² + 5n,   find  its nth term.    Ans  [4n + 3]

(b) In an AP, If Sn =   3n² + n. Find its 22^nd term.   Ans [130]

(c) In an AP If Sn =  3n² + 6n. Find its nth term.     Ans [6n + 3]

(d) In an AP If Sn  = 5n² + 3n. Find its nth term.     Ans [10n - 2]

(e) In an AP If Sn  = 4n² - 3n.. Find its nth term.     Ans [8n-7]

Question 17: The 6^th term of an AP is -10 and 10^th term is -26. Find the 15^th term of the AP

[Ans: - 46]

Question 18 : 

(a) Find the sum of all two digit no. Which are divisible by 4. 

Ans [1188]

(b) Find the sum of all multiple of 8 lying between  201 and 950.

(c) Find the sum of all natural no. Between 100 & 300 which are divisible by 6 

Ans [6534]

(d) Find the sum of all natural no. Between 200 & 300 which are divisible by 4 

Ans [6000]

(e) Find the sum of all integers between 50 & 500 which are divisible by 7  

Ans [17696]

(f) Find the sum of first hundred even natural number which are divisible by 5. 

Ans [50500]

(g) Find the sum of all 3 digit no. Which leaves remainder 3 when divided by 5 

Ans [99090]

(h) 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 19: Find the no. Of terms of an AP: 54, 51, 48....... so that their sum is  513.          

Ans [18 or 19]

Question 20: Which term of the AP: 5, 9, 13, 17.....is 81 also find their sum.                          

Ans [20^th , 860]

Question 21: 

(a) The 5^th term of  an AP is zero. Show that its 33^rd term is 4 times its 12^th term.

(b) If 8^th term of an AP is zero. Prove that its 38^th term is triple its 18^th term.

Question 22: 

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

Ans[1] 

Question 23: Find the 9^th term from the end of the AP:   5, 9, 13, …….185.                      

Ans [153]

Question 24: Find the sum of 11 terms of an AP whose middle term is 30.                              

Ans [330]

Question 25: 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 26: Find the common difference of an AP whose 1^st term is 100 and the sum of whose first 6 terms  is 5 times  the sum of next 6 terms.  

Ans [-10]

Question 27: The ratio of the 7^th to the 3^rd term of an AP is 12 : 5 Find t₁₃  :  t₁₄   

 Ans [90 : 97]

Question 28: 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 29: Sum of 3 terms of an AP is  21 and their product is 231. Find the numbers.        

Ans [3, 7, 11]

Question 30:Find 4 numbers in AP whose sum is 20 and sum of whose square is  120.            

Ans [2, 4, 6, 8]

Question 31: The first and last term of an AP is a  & l show that sum of the n^th term from the beginning and n^th term from the last is a + l.

Question 32: 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 33: The angles of a triangle are in AP. The greatest angle is twice  the least. Find the angles of the triangle. 

Ans[40^o, 60^o and 80^o]

Question 34: If 7 time the 7^th term of an Ap is equal to the 11 times  the 11^th term. Show that the 18^th term of the AP is zero.

Question 35: If m times the m^th term of an AP is equal to the n times of the n^th term then show  that  its    (m + n)^th is zero.

Question 36: 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 37: The ratio of the 10^th term to its 30^th 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 38: The sum of first and 8^th 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 39: 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 40: 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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