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QUESTION: 1

The 5^{th} term of the sequence is

Solution:

a_{n} = (n^{2})/2^{n}

⇒ a_{5} = [(5)^{2}]/2^{(5)}

⇒ a_{5} = 25/32

QUESTION: 2

A sequence is a function whose domain is the set of

Solution:

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.

QUESTION: 3

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

Solution:

QUESTION: 4

The first 4 terms of the sequence a_{1} = 2, a_{n} = 2a_{n-1} + 1 for n __>__ 2 are

Solution:

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………

QUESTION: 5

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

Solution:

an = (n-1)(2-n)(3+n)

Put n = 10

an = 9×(-8)×13

= - 936

QUESTION: 6

The 10^{th} term of the sequence a_{n} = 2(n -1)(2n - 1) is

Solution:

an = 2(n -1)(2n - 1)

a10 = 2(10-1)(2(10)-1))

= 2(9)(19)

= 342

QUESTION: 7

The sum of the series for the sequence a_{n} = (2n-1)/2, for 1 __<__ n __<__ 5 is

Solution:

Put n=1 then a_{1}=1/2

then put n=2 a_{2}=3/2

put n=3 a_{3}=5/2

n=4 a_{4}=7/2

n=5 a_{5}=9/2

their sum is 25/2

QUESTION: 8

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

Solution:

How do we get from 2 to 6? One way is to multiply by 3.

How do we get from 6 to 18? We can multiply by 3 once again.

What about 18 to 54? Again, we can multiply by 3.

We notice that our common ratio is 3. We can leverage this fact to write the next terms of our sequence:

...54,(54⋅3),(54⋅32),(54⋅33)

Notice, we are multiplying by three every time. The 7th term of this sequence is given by the blue expression

54⋅33, which is equal to

54⋅27=1458

QUESTION: 9

The sequence whose terms follow the certain pattern is called a

Solution:

Those sequences whose terms follow certain patterns are called progressions

QUESTION: 10

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

Solution:

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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