Class 10 Maths Important Questions for Arithmetic Progression

Given below are the Class 10 Maths Important Questions for Arithmetic Progression
a. Concepts questions
b. Calculation problems
c. Long answer questions
d. proof questions
Question 1
The general term of a sequence is given by an = -4n + 15. Is the sequence an A. P.? If so, find its 15th term and the common difference.

Question 2
The nth term of an A. P. is 6n + 11. Find the common difference.

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

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

Question 5
Which term of the A. P. 3, 15, 27, 39...... will be 132 more than its 54th term?

Question 6
Two A. P.’s has the same common difference. The difference between their 100th terms is 111222333. What is the difference between their Millionth terms?

Question 7
The 10th and 18th terms of an A. P. are 41 and 73 respectively. Find 26th term.

Question 8
If (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.

Question 9
If the nth term of the A. P. 9, 7, 5.... is same as the nth term of the A. P. 15, 12, 9...... find n.

Question 10
Find the second term and nth term of an A. P. whose 6th term is 12 and the 8th term is 22.

Question 11
The sum of 4th and 8th terms of an A. P. is 24 and the sum of 6th and 10th terms is 34. Find the first term and the common difference of the A. P.

Question 12
If an A. P. consists of n terms with first term a and nth term l show that the sum of the nth term from the beginning and the mth term from the end is (a + l).
Question 13
If the ath term of an A. P. be 1/b and bth term be 1/a then show that its (ab)th term is 1.
Question 14
If the pth term of an A. P. is q and the qth term is p. Prove that its nth term is (p + q – n)
Question 15
If m times the mth 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.

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) $1+n+n^2$

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Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20