# Class 10 Arithmetic Progressions Previous Years Questions

**Arithmetic Progressions Previous Years Questions**

- For what value of k will k + 9, 2k – 1 and 2k + 7 are the consecutive terms of an A.P. ?
**[CBSE 2016] [1 Mark]** - In an AP, if the common difference is -4 and the seventh term is 4, then find the first term.
**[CBSE 2018] [1 Mark]** - Find the sum of the first 10 multiples of 3.
**[CBSE 2019] [1 Mark]** - Find the sum of the first 10 multiples of 6.
**[CBSE 2019] [1 Mark]** - The first term of an A.P. is 5 and the last term is 45. If the sum of all the terms is 400, the number of terms is
- 20
- 8
- 10
- 16
**[CBSE 2020] [1 Mark]**

- The 9
^{th}term of the A.P. -15, -11, -7, …., 49 is- 32
- 0
- 17
- 13
**[CBSE 2020] [1 Mark]**

- The 4
^{th}term of an A.P. is zero. Prove that the 25^{th}term of the A.P. i three times its 11^{th}term.**[CBSE 2016] [2 Marks]** - Is 67 a term of the A.P. : 7, 10, 13, ……?
**[CBSE 2017] [2 Marks]** - Find the sum of first 8 multiples of 3.
**[CBSE 2018] [2 Marks]** - If the ratio of the sum of first n terms of two A.P’s is (7n + 1) : (4n + 27), find the ratio of their m
^{th}terms.**[CBSE 2016] [3 Marks]** - Find the sum first 34 terms of the AP, whose n
^{th}term is given by a_{n}= 5**–**2n.**[CBSE 2017] [3 Marks]** - If the 6 times the 6
^{th}term of an A.P. is equal to 9 times the 9^{th}term, show that its 15^{th}term is zero.**[CBSE 2020] [3 Marks]** - The sum of the first 30 terms of an A.P. is 1920. If the fourth term is 18, find its 11
^{th}term.**[CBSE 2020] [3 Marks]** - The house in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses proceeding the house numbered X is equal to sum of the numbers of houses following X.
**[CBSE 2016] [4 Marks] [Optional]** - The sum of first 5 terms of an A.P. is 45 and that of its first 15 terms is 435. Find the sum of first n terms of this A.P.
**[CBSE 2017] [4 Marks]** - If the numbers a, b, c, d and e are in A.P. then prove that a – 4b + 6c – 4d + e = 0.
**[CBSE 2017] [4 Marks]** - The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7:15. Find the numbers.
**[CBSE 2018] [4 Marks]** - If m times the m
^{th}term of an Arithmetic Progressions is equal to n times its n^{th}term and m**≠**n, show that the (m + n)^{th}term of the A.P. is zero.**[CBSE 2019] [4 Marks]** - The sum of the first three numbers in an Arithmetic Progressions is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
**[CBSE 2019] [4 Marks]**

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