Primary Series Sequence

The sequence is a set of things that are in order. The sequence goes on to infinite number and it is called an infinite sequence. Otherwise it is finite sequence. They are different sequences like arithmetic, geometric, Triangular sequences these are special sequences. Series representation of sequence depends on the difference between two digits and the difference should be same thought of sequence then represent with mathematical induction formulas and simplify the equation

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Problems on Primary Series Sequence:

The series and sequence contains arithmetic progression, geometric progression, sum of first n natural numbers and sum of square of n natural numbers etc.  The following problems based on these concepts.

Example 1 in primary series sequence:

Problem:

To find general term for given sequence, suggest possible next three terms. The sequence is 8, 16, 24…

Solution:

The given sequence is 8, 16, 24….

The first term = 8.

The common difference is = 16-8=8.

The next three terms in the given sequence =24+8=32, 32+8=40, 40+8=48,

The series are 8, 16, 24, 32, 40, and 48.

Example 2 in primary series sequence:

Problem:

To find the numbers the sum of 3 numbers in GP is 16 and their product is 64.

Solution:

Let the three numbers x/y, x, xy.

x/y + x+ xy =16

(x/y) x (xy) =64.  X3 = 64; x= 4.

x/y(1 + y +y2 )=16

4(1 + y +y2 ) =16y.

4 y2  + 4y -16y +4=0

y2  -3y+1=0

y=2.

Where y=2 then the numbers are 2, 4, 8.

Example 3 in Primary Series Sequence:

Problem:

To find general term for given sequence, suggest possible next four terms. The sequence is 3, 6, 9…

Solution:

The given sequence is 3, 6, 9….

The first term = 3.

The common difference is = 6-3=3.

The four terms in the given sequence =9+3=12, 12+3=15, 15+3=18, 18+3=21.

The series are 3, 6, 9, 12, 15, 18, and 21.

Example 3 in primary series sequence:

Problem:

To find sum to 5th in the sequence numbers in the 2,4,8..

Solution:

Here first term a=2

The ratio r = 4/2=2

Sum =  arn-1

n=5, sum = 2(25-1) =32.