Arithmetic Progression Class 10 Extra Questions

Arithmetic Progression Class 10 Extra Questions

                          CLASS- X CH- 5  ARITHMETIC  PROGRESS                                                         

Multiple Choice Questions

1. The value of x for which 2x, x + 10 and 3x + 2 are three consecutive terms of an AP is
   a) – 6          b) 18           c) 6             d) – 18      
2. 2. If 18, a, b, -3 are in AP, then a + b =
   a) 19                     b) 7             c) 11           d) 15
3. Two APs have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30^th terms is
   a) 11                     b) 3               c) 8           d) 5
4. The sum of first n even natural numbers is
   a) 2n                     b) n²              c) n² + n              d) n² – 1 
5.  If the nth term of an AP is 3n + 7, then its common difference is
   a) 7                       b) 3               c) 3n                   d) 1  
   
6. If nth term of an AP is ( 2n + 1), then the sum of first n terms of the AP is
   a) n(n-2)               b) n(n+2)       c) n(n+1)             d) n(n-1)
7.  If a, b, c form an AP with common difference d, then the value of a – 2b – c is equal to

a) 2a + 4d             b) 0                c) – 2a – 4d          d) – 2a – 3d
8. The 11^th term from the end of the AP : 10, 7, 4, ……, – 62 is :
a) 25                     b) 16           c) – 32                  d) 0
9.  The common difference of an AP in which a₂₁ – a₇ = 84
a) 6                            b) – 6          c) 5                       d) – 5

                           Subjective Type Questions

1.   If pth term of an AP is q and qth  term is p, then prove that its nth term is ( p +   q – n)
2.   Which term of the A.P : 21,18,15………….. is – 18?
3.  Determine A.P whose 3^rd term is 5 and the 7^th term is 9.
4.  How many 2 digit numbers are divisible by 3?
5.  Find the values of a, b and c such that the numbers  a, 10, b, c, 31 are in AP.
6.  If 5 times the fifth term of an AP is equal to eight times its eighth term, show that its 13^th term is zero. 
7.  The 16^th term of an AP is 1 more than twice its 8^th term. If the 12^th term of the AP is 47, then find its nth term.
8.  Find the 11^th term of the A.P from the last term of the A.P:  10, 7,4 ….……-62
9.  What is the sum of first 20 odd natural numbers?
10.  If the sum of first 14 terms of an A.P is 1050 and its first term is 10. Find the 20^th term?
11.  How many terms of the given A.P must be taken so that their sum is 78? 
    24, 21, 18…………………..
12.  Find the sum of first 24 terms of the list of the numbers, whose  n^𝑡ℎ term is given by 𝑎_𝑛=3+2n
13. The sum of first 7 terms of an A.P is 49 and that of 17 terms is 289. Find the sum of first n terms.
14. The first and the last term of an A.P are 17 and 350 respectively. If common difference is 9 then how many terms are there and what is their sum?
15. The 4^th term of an AP is equal to 3 times the first term and the 7^th term exceed twice the 3^rd term by 1. Find the AP. 
16. Find the middle term of the A.P. 6, 13, 20,……216.
17.  Find the sum of all 3-digit natural numbers, which are multiples of 7.
18.   Find the sum of all multiples of 9 lying between 400 and 800.
19. If the sum of n terms of an AP  is 2n² + 5n, then find its 4^th term.
20.  If the sum of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero.
21.  If the m^th term of an A.P. is  n^th term is 1/m , show that the sum of mn terms is    .
22. The sum of first q terms of an AP is 63q – 3q². If its pth term is – 60, find the value of p. Also find the 11^th term of  this AP.
23. The sum of first seven terms of an AP is 182. If its 4^th term and 17^th terms are in the ratio  1: 5, then find the AP.
24. Find the sum of two middle most terms of the AP
25. Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
26. If the 7^th term of an AP is 1/9 and its 9^th term is 1/7, find its 63^rd term.
27.  Assertion: Sum of natural number from 1 to 100 is 5050

Reason: Sum of n natural number is n(n+1)/2

28. Assertion: If S_n is the sum of the first n terms of an A.P., then its nth term is   given by a_n = S_n – S_{n – 1}.
Reason: The 10th term of the A.P. 5, 8, 11, 14, ……………….is 35.

•                                         CASE STUDY  

Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of   Rs 1,18,000 by paying every month starting with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month, answer the following:

(i) Find the amount paid by him in 30^th instalment.
(ii). What amount does he still have to pay after 30^th installment?
(iii). If total installments are 40 then find the amount paid in the last installment?
(iv). Find the ratio of the 1^st installment to the last installment .

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