Question

The algebraic form of an arithmetic sequence is xn=3n+2.
What is its common difference? ​

Answer 1

Answer:

$x_{n}$ =3n +2

substituting n=1

$x_{n}$=3(1) +2=5

substituting n=2,

$x_{n}$=3(2)+2=8

substituting n=3,

$x_{n}$=3(3)+2=11

there fore the A P formed is 5 , 8, 11.......

Common difference is  ,$a_{2} -a_{1}$=8-5=3

the common difference is 3

hope it helps you....

Answer 2

The common difference of the arithmetic sequence is 3

Given :

The algebraic form of an arithmetic sequence is xₙ = 3n + 2

To find :

The common difference of the arithmetic sequence

Solution :

Step 1 of 3 :

Write down nth term of the arithmetic sequence

Here the nth term of an arithmetic sequence is given by

xₙ = 3n + 2

Step 2 of 3 :

Find the AP

Putting n = 1 , 2 , 3 , 4 , . . . . we get the arithmetic sequence as 5 , 8 , 11 , 14 , . . . .

Step 3 of 3 :

Find common difference of the arithmetic sequence

First term = 5

Second Term = 8

Third term = 11

Fourth term = 14

Now common difference is defined as the difference between the successive term and its preceding term.

Then common difference of the AP

= Second Term - First term

= 8 - 5

= 3

Note :

The common difference of the AP can be find as below :

Then common difference of the AP

= nth term of the arithmetic sequence - (n - 1)th term of the arithmetic sequence

= (3n + 2) - [ 3(n - 1) + 2 ]

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

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

= 3n + 2 - 3n + 1

= 3

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