Given below are the Class 10 Maths Important Questions(Short questions) for Arithmetic Progression
a) Concepts questions
b) Calculation problems
c) Multiple choice questions
d) Long answer questions
e) Fill in the blank's Question 1The general term of a sequence is given by a_{n} = -4n + 15. Is the sequence an A. P.? If so, find its 15^{th} term and the common difference. Solution

a_{n} = -4n + 15
a_{k} = -4k + 15
a_{k+1} = -4(k+1) + 15
Now
a_{k+1} - a_{k}=-4(k+1) + 15 -[-4k + 15]=-4
Since difference between two terms constant.It is a AP
a_{15} = -4(15) + 15=-45

Question 2The n^{th} term of an A. P. is 6n + 11. Find the common difference. Solution

Question 3If the 8^{th} term of an A. P. is 31 and the 15^{th} term is 16 more than the 11^{th} term, find the A. P. Solution

a_{8} = 31
a +(8-1)d = 31
a + 7d = 31 -- (i)

a_{15} =16 + a_{11}
a + 14d = 16 + a +10d
14d = 16 + 10d
4d = 16
d = 4
Now putting d = 4 in eq. (i) we get
a + 7(4) = 31
a + 28 = 31
a = 3

So AP
3,7,11,15...

Question 4Which term of the arithmetic progression 5, 15, 25, ----- will be 130 more than its 31^{st} term? Solution

Let n th term be 130 more than the 31st term of the A.P.
First term of A.P. = 5
Common difference = 15 – 5 = 10
a_{n} = 130 + a_{31}
5 + (n – 1) X 10 = 130 + 5 + (31 – 1) X 10
10 (n – 1) = 430
n = 44

Thus, 44th term of the A.P is 130 more than the 31st term.

Question 5Which term of the A. P. 3, 15, 27, 39…… will be 132 more than its 54^{th} term? Question 6Two A. P.’s has the same common difference. The difference between their 100^{th} terms is 111 222 333. What is the difference between their Millionth terms? Question 7The 10^{th} and 18^{th} terms of an A. P. are 41 and 73 respectively. Find 26^{th} term. Question 8If (m + 1)^{th} term of an A. P. is twice the (n + 1)^{th} term. Prove that the (3m + 1)^{th} term is twice the (m + n + 1)^{th }term. Solution

(m+1)th term= a + (m+1-1) d = a + m d
(n +1) th term = a+ (n+1-1) d = a + n d
now given condition is
a+ md = 2 ( a + n d ) ---- (1)

Now
(3m + 1) th term = a + (3m+1-1) d= a + 3m d -- (2)
(m+n+1) th term = a + (m+n +1 -1) d = a + (m+n) d ---(3)

Now
(3m+1)th term= a +3md
=a +md + 2md
Now we have a+md = 2 (a + nd ) from equation 1
=2(a+nd) + 2md
= 2(a + nd + md)
= 2(a +(m+n)d )
=2 (m+n+1) th ( from (3) )
Hence proved

Question 9If the n^{th} term of the A. P. 9, 7, 5… is same as the n^{th} term of the A. P. 15, 12, 9…. find n. Question 10Find the second term and n^{th }term of an A. P. whose 6^{th} term is 12 and the 8^{th} term is 22. Question 11 The sum of 4^{th} and 8^{th} terms of an A. P. is 24 and the sum of 6^{th} and 10^{th} terms is 34. Find the first term and the common difference of the A. P. Question 12If an A. P. consists of n terms with first term a and n^{th} term l show that the sum of the n^{th} term from the beginning and the m^{th} term from the end is (a + l). Question 13If the a^{th }term of an A. P. be 1/b and b^{th} term be 1/a then show that its (ab)^{th} term is 1. Question 14If the p^{th} term of an A. P. is q and the q^{th} term is p. Prove that its nth term is (p + q – n) Question 15If m times the m^{th} term of an A. P. is equal to n times its nth term. Show that the (m + n)^{th} term of the A. P. is zero. Solution

According to the question
m(a_{m} ) = n(a_{n})
Now for a,d as first term and common difference of the AP,nth term is defined as ,
a_{n} = a + (n-1)d
So
m[a + (m-1)d] = n[a + (n-1)d]
[ma + (m^{2} - m)d]= [na + (n^{2} - n)d]
[ma + (m^{2}d- md)]= [na + (n^{2}d- nd)]
[ma-na] + [m^{2}d- n^{2}d] + [nd-md] = 0
a[m-n] + d[m^{2} - n^{2}] + d[n-m] = 0
Now we know that x^{2} - y^{2} = (x+y) (x-y)
a[m-n] + d[(m+n) (m-n)] - d[m - n] = 0
Divide the above equation with (m-n) ,We get :
a + d(m+n) - d = 0
a + [ (m+n) - 1 ] d = 0
So a_{m+n} = 0

Question 16 Justify whether it is true to say that the following are the nth terms of an AP.
(i) 2n–3
(ii) 3n^{2}+5
(iii) 1+n+n^{2}

4) n =44
5) 65^{th} term is 132 more than its 54^{th} term
6) The difference between millionth terms is same as the difference between 100^{th} term i.e, 11122233
7) 105
9. 7
10. a_{2} = -8, a_{n} = 5n – 18
11. -1/2, 5/2

link to this page by copying the following text

Reference Books for class 10

Given below are the links of some of the reference books for class 10 math.

You can use above books for extra knowledge and practicing different questions.

Note to our visitors :-

Thanks for visiting our website. From feedback of our visitors we came to know that sometimes you are not able to see the answers given under "Answers" tab below questions. This might happen sometimes as we use javascript there. So you can view answers where they are available by reloding the page and letting it reload properly by waiting few more seconds before clicking the button.
We really do hope that this resolve the issue. If you still hare facing problems then feel free to contact us using feedback button or contact us directly by sending is an email at [email protected]
We are aware that our users want answers to all the questions in the website. Since ours is more or less a one man army we are working towards providing answers to questions available at our website.