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Test Level 1: Progressions, Sequences & Series - 1 - CAT MCQ


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10 Questions MCQ Test Level-wise Tests for CAT - Test Level 1: Progressions, Sequences & Series - 1

Test Level 1: Progressions, Sequences & Series - 1 for CAT 2024 is part of Level-wise Tests for CAT preparation. The Test Level 1: Progressions, Sequences & Series - 1 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 1: Progressions, Sequences & Series - 1 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 1: Progressions, Sequences & Series - 1 below.
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Test Level 1: Progressions, Sequences & Series - 1 - Question 1

Find the value of 12 + 1 + 22 + 2 + 32 + 3 + ... + n2 + n.

Detailed Solution for Test Level 1: Progressions, Sequences & Series - 1 - Question 1

The nth term of the given series is tn = n2 + n, n = 1, 2, 3, ..., n

Test Level 1: Progressions, Sequences & Series - 1 - Question 2

Susan had arranged to pay off her debt of $3,600 to CASA Bank in 40 monthly installments in the form of an A.P. When 30 of the installments had been repaid, she died leaving one third of the debt unpaid. What was the value of the first installment?  

Detailed Solution for Test Level 1: Progressions, Sequences & Series - 1 - Question 2

If $a is the first installment and the common difference is $d,
Then,
Sum of n terms

Sum of all installments 

= total debt = 3,600
⇒ 2a + 39d = 180 …(1)

of the total debt = 2400.
⇒ 2a + 29d = 160 …(2)
Subtracting (2) from (1), we get, 10d = 20.
∴ d = 2
∴ a = $51

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Test Level 1: Progressions, Sequences & Series - 1 - Question 3

Detailed Solution for Test Level 1: Progressions, Sequences & Series - 1 - Question 3


Test Level 1: Progressions, Sequences & Series - 1 - Question 4

Find the value of    ..........… 50 terms.

Detailed Solution for Test Level 1: Progressions, Sequences & Series - 1 - Question 4

50th term =
Then, 

Test Level 1: Progressions, Sequences & Series - 1 - Question 5

Find the sum of the infinite series: 1/3 + 3/9 + 7/27 + 15/81 + ............

Detailed Solution for Test Level 1: Progressions, Sequences & Series - 1 - Question 5

The given series can be written as:

Test Level 1: Progressions, Sequences & Series - 1 - Question 6

If a, b, c and d are in GP, then (a - c)2 + (b - c)2 + (b - d)2 is equal to  

Detailed Solution for Test Level 1: Progressions, Sequences & Series - 1 - Question 6

If a, b, c and d are in GP, then
b2 = ac, c2 = bd and ad = bc.
Given equation is:
a2 + c2 - 2ac + b2 + c2 - 2bc + b2 + d2 - 2bd
= [a2 + 2b2 + 2c2 + d2 - 2ac - 2bc - 2bd]
= [a2 + d2 + 2ac + 2bd - 2ac - 2bc - 2bd]
= [a2 + d2 - 2ad] = (a - d)2

Test Level 1: Progressions, Sequences & Series - 1 - Question 7

The ninth term of an AP is 5 more than the sixth term. If the eleventh term of that AP is 35, then what is its first term?

Detailed Solution for Test Level 1: Progressions, Sequences & Series - 1 - Question 7

t9 = t6 + 5
⇒ a + 8d = a + 5d + 5
⇒ d = 5/3
t11 = a + 10d = 35

Test Level 1: Progressions, Sequences & Series - 1 - Question 8

If x, y, z are in AP, then 

Detailed Solution for Test Level 1: Progressions, Sequences & Series - 1 - Question 8

x, y, z are in AP.
∴ 2y = (z + x)
Add (z + x) both sides.
2y + (z + x) = 2(z + x)
⇒ 2(z + x) = (y + z) + (x + y)
⇒ (y + z), (z + x), (x + y) are in AP.

Test Level 1: Progressions, Sequences & Series - 1 - Question 9

The sum of 5 numbers in AP is 75 and the product of the greatest and the least of them is 161. What is the greatest number?

Detailed Solution for Test Level 1: Progressions, Sequences & Series - 1 - Question 9

Let the numbers be a - 2d, a - d, a, a + d, a + 2d.
Then, 5a = 75
a = 15
(a - 2d).(a + 2d) = 161
This implies, d = +4
Greatest term = 15 + 2 x 4 = 23
The greatest term would be the 5th term, if d = +4, and the 1st term, if d = -4.

Test Level 1: Progressions, Sequences & Series - 1 - Question 10

The sum of the 9th, 14th and 18th terms of an AP is equal to the sum of the 20th and 24th terms. What is the ratio of the 4th term to the 2nd term?

Detailed Solution for Test Level 1: Progressions, Sequences & Series - 1 - Question 10

T9 + T14 + T18 = T20 + T24
⇒ 3a + 38d = 2a + 42d
⇒ a = 4d

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