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Maths 1 Marks Question

Arithmetic Progressions · Jharkhand Board (JAC) STD 10 (Jharkhand - English Medium). 7 questions.

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Question 11 Mark
Which of the following form an AP? Justify your answer.
1, 1, 2, 2, 3, 3, .....
Answer
Given form of numbers will form an A.P. If $d_1 = d_2 = d_3....$
$So, d_1 = 1 - 1$
$d_1 = 0$
$d_2 = 2 - 1$
$d_2 = 1$
$\therefore\text{d}_{1}\neq\text{d}_{2}$
Hence, the given form of numbers will form an A.P.
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Question 21 Mark
Which of the following form an AP? Justify your answer.
11, 22, 33, .......
Answer
Given form of numbers will form an A.P. If $d_1 = d_2 = d_3 =......$
$So, d_1 = 22 - 11$
$d_1 = 11$
$d_2 = 33 - 22$
$d_2 = 11$
$d_1 = d_2 = 11$
Hence, the given form of numbers will form an A.P.
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Question 31 Mark
Which of the following form an AP? Justify your answer.
$\frac{1}{2},\frac{1}{3},\frac{1}{4},... $
Answer
Given form of numbers will form an A.P. If $d_1 = d_2 = d_3 =.....$
$\text{So},\text{ d}_{1}=\frac{1}{3}-\frac{1}{2}=\frac{2-3}{6}=\frac{-1}{6}$
$\text{d}_{2}=\frac{1}{4}-\frac{1}{3}=\frac{3-2}{12}=\frac{-1}{12}$
$\therefore\text{d}_{1}\neq\text{d}_{2}$
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Question 41 Mark
Which of the following form an AP? Justify your answer.
-1, -1, -1, -1 ...
Answer
A series of numbers will be in A.P. If $d_1 = d_2 = d_3......$
$So, d_1 = -1 - 1(-1) = 0$
$d_2 = -1 - (-1) = 0$
$d_3 = -1 - (-1) = 0$
$\therefore$ $d_1 = d_2 = d_3.....$
So, the given series form an A.P.
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Question 51 Mark
Which of the following form an AP? Justify your answer.
$2, 2^2, 2^3, 2^4, .......$
Answer
Given form of numbers will form an A.P. If $d_1 = d_2 = d_3....$
$So, d_1 = 2^2 - 2 = 4 - 2$
$d_2 = 2^3 - 2^2 = 8 - 4 = 4$
$d_3 = 2^4 - 2^3 = 16 - 8 = 8$
$\therefore\text{d}_{1}\neq\text{d}_{2}\neq\text{d}_{3}$
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Question 61 Mark
Which of the following form an AP? Justify your answer.
0, 2, 0, 2, .....
Answer
Given form of numbers will be in A.P. If $d_1 = d_2 = d_3......$
$So, d_1= 2 - 0$
$d_1 = 2$
$d_2 = 0 - 2$
$d_2 = -2$
$\therefore\text{d}_{1}\neq\text{d}_{2}$
So, the given of numbers is not an A.P.
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