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Test: Introduction To Sequences - JEE MCQ


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10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Introduction To Sequences

Test: Introduction To Sequences for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Introduction To Sequences questions and answers have been prepared according to the JEE exam syllabus.The Test: Introduction To Sequences MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Introduction To Sequences below.
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Test: Introduction To Sequences - Question 1

The 5th term of the sequence is

Detailed Solution for Test: Introduction To Sequences - Question 1

an = (n2)/2n
⇒ a5 = [(5)2]/2(5)
⇒ a5 = 25/32

Test: Introduction To Sequences - Question 2

A sequence is a function whose domain is the set of

Detailed Solution for Test: Introduction To Sequences - Question 2

The correct option is A.

A sequence is an enumerated collection of objects in which repetitions are allowed and order does matter. Like a set, it contains members. The number of elements is called the length of the sequence. A sequence is a function whose domain is the set of natural numbers or a subset of the natural numbers.

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Test: Introduction To Sequences - Question 3

The arithmetic mean between a and 10 is 30, the value of ‘a’ should be

Detailed Solution for Test: Introduction To Sequences - Question 3

Test: Introduction To Sequences - Question 4

The first 4 terms of the sequence a1 = 2, an = 2an-1 + 1 for n > 2 are

Detailed Solution for Test: Introduction To Sequences - Question 4

a1 = 2 
a2 = 2a1 + 1
=> 2(2) + 1 = 5
a3 = 2a2 + 1
=> 2(5) + 1 = 11
a4 = 2a3 + 1
=> 2(11) + 1 = 23
Hence, the required series is : 2,5,11,23………

Test: Introduction To Sequences - Question 5

What is the 10th term of the sequence defined by an = (n-1)(2-n)(3+n)?

Detailed Solution for Test: Introduction To Sequences - Question 5

an = (n-1)(2-n)(3+n)
Put n = 10
an = 9×(-8)×13
= - 936

Test: Introduction To Sequences - Question 6

The 10th term of the sequence an = 2(n -1)(2n - 1) is

Detailed Solution for Test: Introduction To Sequences - Question 6

an = 2(n -1)(2n - 1) 
a10 = 2(10-1)(2(10)-1))
= 2(9)(19)
= 342

Test: Introduction To Sequences - Question 7

The sum of the series for the sequence an = (2n-1)/2, for 1 < n < 5 is

Detailed Solution for Test: Introduction To Sequences - Question 7

Put n=1 then a1=1/2  

then put n=2 a2=3/2

 put n=3 a3=5/2

 n=4 a4=7/2

 n=5 a5=9/2

 their sum is 25/2

Test: Introduction To Sequences - Question 8

7th term of Geometric Progression 2, 6, 18, ... is

Detailed Solution for Test: Introduction To Sequences - Question 8

The 7th term of a geometric progression (GP) can be found using the formula:

Tn=a⋅rn−1

Where:

  • Tn​ is the n-th term,
  • a is the first term,
  • r is the common ratio,
  • n is the term number.

In the given GP: 2, 6, 18, ...

  • The first term a=2
  • The common ratio r=6/2=3

Now, substitute into the formula for the 7th term:

T= 2⋅37−1 = 2⋅3= 2⋅729 = 1458

So, the 7th term is 1458

Test: Introduction To Sequences - Question 9

The sequence whose terms follow the certain pattern is called a

Detailed Solution for Test: Introduction To Sequences - Question 9

Those sequences whose terms follow certain patterns are called progressions

Test: Introduction To Sequences - Question 10

A sequence in which (any term) − (its immediate previous term) gives a constant is called

Detailed Solution for Test: Introduction To Sequences - Question 10

An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant.

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