- Introduction
- |
- What is arithmetic progression
- |
- Some Important points about AP
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- nth term of Arithmetic Progression
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- Sum of nth item in Arithmetic Progression

Given below are the **Class 10 Maths** Important Questions(Short questions) for Arithmetic Progression

b) Calculation problems

c) Multiple choice questions

d) Long answer questions

e) Fill in the blank's

- The 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. - The n
^{th}term of an A. P. is 6n + 11. Find the common difference. - If 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. - Which term of the arithmetic progression 5, 15, 25, ----- will be 130 more than its 31
^{st}term? - Which term of the A. P. 3, 15, 27, 39…… will be 132 more than its 54
^{th}term? - Two 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? - The 10
^{th}and 18^{th}terms of an A. P. are 41 and 73 respectively. Find 26^{th}term. - 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. - If 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. - Find the second term and n
^{th }term of an A. P. whose 6^{th}term is 12 and the 8^{th}term is 22. - 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. - If 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). - If 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. - If 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) - If 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. - 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}

**Answer**

1) -45, -4

2) 6

3) A. P. is 3, 7, 11, 15, 19

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

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