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Sequences and Series — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSSequences and Series3 Marks
Question
Match the questions given under Column I with their appropriate answers given under the Column II.
Column I
Column II
(a)
$4,1,\frac{1}{4},\frac{1}{16}$
(i)
A.P.
(b)
2, 3, 5, 7
(ii)
Squence
(c)
13, 8, 3, -2, -7
(iii)
G.P.
✓

Answer
Column I
Column II
(a)
$4,1,\frac{1}{4},\frac{1}{16}$
(i)
G.P.
(b)
2, 3, 5, 7
(ii)
Squence
(c)
13, 8, 3, -2, -7
(iii)
A.P.
Solution:
  1. $4,1,\frac{1}{4},\frac{1}{16}$
Here, $\frac{\text{a}_2}{\text{a}_1}=\frac{1}{4},\frac{\text{a}_3}{\text{a}_2}=\frac{\frac{1}{4}}{1}=\frac{1}{4}$ and $\frac{\text{a}_4}{\text{a}_3}=\frac{\text{a}_4}{\text{a}_3}=\frac{\frac{1}{16}}{\frac{1}{4}}=\frac{1}{4}$ Hence, it is G.P.
  1. 2, 3, 5, 7
Here, a2 - a1 = 3 - 2 = 1 a3 - a2 = 5 - 3 = 2 $\therefore\ \text{a}_2-\text{a}_1\neq\text{a}_3-\text{a}_2$ Hence, it is not A.P. $\frac{\text{a}_2}{\text{a}_1}=\frac{3}{2},\frac{\text{a}_3}{\text{a}_2}==\frac{5}{3}$ So, $\frac{3}{2}\neq\frac{5}{3}$ So, it is not G.P. Hence, it is squence.
  1. 13, 8, 3, -2, -7
Here, a3 - a1 = 8 - 13 = -5 a3 - a2 = 3 - 8 = -5 So, a2 - a1 = a3 - a2 = -5 So, it is an A.P.

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