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QUESTION: 1

The 5^{th} term of the sequence is

Solution:

QUESTION: 2

A sequence is a function whose domain is the set of

Solution:

A sequence is a function whose domain is the set of natural numbers or a subset of the natural numbers. We usually use the symbol an to represent a sequence, where n is a natural number and an is the value of the function on n.

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:

QUESTION: 5

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

Solution:

QUESTION: 6

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

Solution:

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 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

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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