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Class 10 Maths Important Questions(Short questions) for Arithmetic Progression



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
  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.
  2. The nth term of an A. P. is 6n + 11. Find the common difference.
  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.
  4. Which term of the arithmetic progression 5, 15, 25, ----- will be 130 more than its 31st term?
  5. Which term of the A. P. 3, 15, 27, 39…… will be 132 more than its 54th term?
  6. Two A. P.’s has the same common difference. The difference between their 100th terms is 111 222 333. What is the difference between their Millionth terms?
  7. The 10th and 18th terms of an A. P. are 41 and 73 respectively. Find 26th term.
  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.
  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.
  10. Find the second term and nth term of an A. P. whose 6th term is 12 and the 8th term is 22.
  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.
  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).
  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.
  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)
  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.
  16.  Justify whether it is true to say that the following are the nth terms of an AP.
(i) 2n–3
(ii) 3n2+5
(iii) 1+n+n2
Answer
1) -45, -4
2) 6
3) A. P. is 3, 7, 11, 15, 19
4) n =44
5) 65th term is 132 more than its 54th term
6) The difference between millionth terms is same as the difference between 100th term    i.e, 11122233
7) 105
9. 7
10. a2 = -8, an = 5n – 18
11. -1/2, 5/2


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