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Arithmetic Progressions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions4 Marks
Question
A sequence is an ordered list of numbers. A sequence of numbers such that the difference between the consecutive terms is constant is said to be an arithmetic progression (A.P.). On the basis of above information, answer the following questions.
  1. Which of the following sequence is an A.P.?
  1. 10, 24, 39, 52,....
  2. 11, 24, 39, 52, ...
  3. 10, 24, 38, 52, ...
  4. 10, 38, 52, 66, ....
  1. If x, y and z are in A.P., then.
  1. x + z = y
  2. x - z = y
  3. x + z = 2y
  4. None of these
  1. If $a_1, a_2 ..... a_3$ are in A.P. then which of the following is true?
  1. $a_1 + k, a_2 + k, a_3 + k.....,a_n$ k are in A.P., where k is a constant.
  2. $k - a_1, k - a_{2,} k - a_3......,k - a_n​​​​​​​$ are in A.P., where k is a constant.
  3. $ka_1, ka_2, ka_3........,ka_n​​​​​​​$ are in A.P., where k is a constant.
  4. All of these
  1. If the $n^{th}​​​​​​​$​​​​​​​ term (n > 1) of an A.P. is smaller than the first term, then nature of its common difference (d) is.
  1. d > 0
  2. d < 0
  3. d = 0
  4. Can't be determined
  1. Which of the following is incorrect about A.P.?
  1. All the terms of constant A.P. are same.
  2. Some terms of an A.P. can be negative.
  3. All the terms of an A.P. can never be negative.
  4. None of these.
✓

Answer

  1. (c) 10, 24, 38, 52,....
  2. (c) x + z = 2y
  3. (d) All of these
  4. (b) x - z = y
  5. (c) All the terms of an A.P. can never be negative.

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