This EduRev document offers 10 Multiple Choice Questions (MCQs) from the topic Progressions, Sequences & Series (Level - 2). These questions are of Level - 2 difficulty and will assist you in the preparation of CAT & other MBA exams. You can practice/attempt these CAT Multiple Choice Questions (MCQs) and check the explanations for a better understanding of the topic.
Question for Practice Questions Level 2: Progressions, Sequences & Series - 1
Try yourself:The interior angles of a polygon are in A.P. If the least angle is 42° and common difference is 33°, the number of sides is
Explanation
Given: a = 42°, d = 33°
Sum of all the interior angles of an n-sided polygon is (n - 2)180°.
(n - 2) × 180 = (n/2)(2 × 42 + (n - 1) × 33)
360n - 720 = 84n + 33n2 - 33n
11n2 - 103n + 240 = 0
(n - 5)(11n - 48) = 0
This implies, n = 5 as sides can't be fraction in number.
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Question for Practice Questions Level 2: Progressions, Sequences & Series - 1
Try yourself:If the sum of the series 1 + 3/x +9/x2 + 27/x3 + … to infinity exists, then which of the following must be true?
(Given that x is not less than or equal to zero)
Explanation
Since the sum to infinity of the given GP exists, so its common ratio should be 0 < |3/x| < 1.
0 < 3/x is always true because x > 0.
3/x < 1
or
or
x > 3
According to question, x is not negative.
So, x > 3
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Question for Practice Questions Level 2: Progressions, Sequences & Series - 1
Try yourself:If x, y, z are in A.P, then (x + 2y - z)(2y + z - x)(z + x - y) equals
Explanation
x, y, z are in A.P.
Therefore, 2y = x + z
Given equation: (x + 2y - z)(2y + z - x)(z + x - y)
= (x + x + z - z)(x + z + z - x)(2y - y)
= 2x(2z)(y) = 4xyz
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Question for Practice Questions Level 2: Progressions, Sequences & Series - 1
Try yourself:In a GP, the third term is 10 more than the second term and the second term is 6 more than the first term. What is the fifth term?
Explanation
T3 - T2 = ar2 - ar = 10
⇒ ar(r - 1) = 10
and T2 - T1 = 6, or ar - a = 6
⇒ a(r - 1) = 6
r = 10/6 = 5/3 and a = 9
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Question for Practice Questions Level 2: Progressions, Sequences & Series - 1
Try yourself:If the sum of the first 8 terms of an AP is exactly half of the sum of the next 8 terms, what is the ratio of the 16th term to the 8th term of the AP?
Explanation
4a + 14d = 2a + 23d
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Question for Practice Questions Level 2: Progressions, Sequences & Series - 1
Try yourself:Sweety purchased a box of chocolates. She ate 1 chocolate on the first day, 3 on the second day, 6 on the third day, 10 on the fourth day and so on. Finally, she finished all the chocolates in exactly 20 days. How many chocolates were there in the box?
Explanation
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Question for Practice Questions Level 2: Progressions, Sequences & Series - 1
Try yourself:The sums of odd and even numbered terms of an infinite GP are in the ratio of 3 : 2. What is the common ratio (r)?
Explanation
Let the GP be a, ar, ar2, ar3, ………….
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Question for Practice Questions Level 2: Progressions, Sequences & Series - 1
Try yourself:If log3 2, log3 (2x - 5) and log3 (2x - 7/2) are in arithmetic progression, then the value of x is equal to
Explanation
Since log3 (2), log3 (2x - 5) and log3 are in AP, therefore we can write:
∴ log3 (2x - 5)2 = log3 (2x + 1 - 7)
∴ (2x - 5)2 = 2x + 1 - 7
Let, 2x = y.
Then, (y - 5)2 = 2y - 7
⇒ y2 + 25 - 10y = 2y - 7
⇒ y2 - 12y + 32 = 0
⇒ (y - 8)(y - 4) = 0
We get, 2x = 8 and 2x = 4
⇒ x = 3 and 2
If x = 2, then 2x - 5 = 4 - 5 = -1< 0, not possible
So x = 3
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Question for Practice Questions Level 2: Progressions, Sequences & Series - 1
Try yourself: up to 50 terms is equal to
Explanation
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Question for Practice Questions Level 2: Progressions, Sequences & Series - 1
Try yourself:
Explanation
The nth term of the given series is tn
The sum of the series is
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