Test: Introduction To Sequences - JEE MCQ

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

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.

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………

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

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

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

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:

T₇ = 2⋅3⁷⁻¹ = 2⋅3⁶ = 2⋅729 = 1458

So, the 7th term is 1458

Those sequences whose terms follow certain patterns are called progressions

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.