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Arithmetic Progressions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions4 Marks
Question
Jack is much worried about his upcoming assessment on A.P. He was vigorously practicing for the exam but unable to solve some questions. One of these questions is as shown below. If the $3^{rd}$​​​​​​​ and the $9^{th}​​​​​​​$​​​​​​​ terms of an A.P. are 4 and - 8 respectively, then help Jack in solving the problem.
  1. What is the common difference?
  1. 2
  2. -1
  3. -2
  4. 4
  1. What is the first term?
  1. 6
  2. 2
  3. -2
  4. 8
  1. Which term of the A.P. is -160?
  1. $80^{th}$
  2. $85^{th}$
  3. $81^{th}$
  4. $84^{th}$
  1. Which of the following is not a term of the given A.P.?
  1. -123
  2. -100
  3. 0
  4. -200
  1. What is the $75^{lh}​​​​​​​$​​​​​​​ term of the A.P.?
  1. -140
  2. -102
  3. -150
  4. -158
✓

Answer

We have, $3^{\text {rd }}$ term $=4$ and $9^{\text {th }}$ term $=-8$ i.e., $a+2 d=4$ and $a+8 d=-8$ Solving (1) and (2), we get $d=-2, a=8$
  1. (c) -2
  2. (d) 8
  3. (b) $85^{th}$​​​​​​​
Solution:
Let $t_n= -160$
$\Rightarrow a + (n - 1) d = -160$
$\Rightarrow 8 + (n - 1)(-2) = -160$
$\Rightarrow (n - 1)(-2) = -168$
$\Rightarrow n - 1 = 84$
$\Rightarrow n = 85$
So, $t_{85} = -160​​​​​​​$​​​​​​​
  1. (a) -123
  2. (a) -140
Solution:
$t_{75} = a + 74d = 8 + 74(-2) = -140$

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