Question

I really need help with this math problem

Answer 1

`(1)/(5)`

Common difference of the given arithmetic sequence is equal to
`(1)/(5)`

Explanation:

The given arithmetic sequence is in mixed numbers. Converting them into proper fractions, we get:

`First\ term = t_1 = -2\\\\Second\ term = t_2 = -1(4)/(5) = -((5*1)+4)/(5) = -(9)/(5)\\\\Third\ term = t_3 = -1(3)/(5) = -((5*1)+3)/(5) = -(8)/(5)\\\\Fourth\ term=t_4 = -1(2)/(5) = -((5*1)+2)/(5) = -(7)/(5)`

The sequence can thus be rewritten as
`-2, -(9)/(5), -(8)/(5), -(7)/(5)`

To find the common difference of the given arithmetic sequence, subtract any two consecutive numbers of the sequence. The difference between two consecutive numbers is always a constant and is termed as the common difference.

Hence,

`d_1= t_2-t_1=(-(9)/(5) -(-2)= (-9+10)/(5)= (1)/(5) \\\\d_2=t_3-t_2= (-(8)/(5) -(-(9)/(5) )= (-8+9)/(5) = (1)/(5)\\\\d_3=t_4-t_3= (-(7)/(5) -(-(8)/(5) )= (-7+8)/(5) = (1)/(5)`

`d_1=d_2=d_3 = d`

Common difference
`d=(1)/(5)`

Answer 2

Common difference =
`(1)/(5)`

Solution:

Given arithmetic sequence:

`$-2,-1(4)/(5) ,-1(3)/(5) , -1(2)/(5) , ....`

Let us first convert the improper fraction into mixed fraction.

`$-2,-(9)/(5) ,-(8)/(5) , -(7)/(5) , ....`

Difference between two numbers in an arithmetic sequence is the common difference.

`$a_2-a_1=-(9)/(5)-(-2)=-(9)/(5)+2=(1)/(5)`

`$a_3-a_2=-(8)/(5)-\left(-(9)/(5)\right)=-(8)/(5)+(9)/(5)=(1)/(5)`

`$a_4-a_3=-(7)/(5)-\left(-(8)/(5)\right)=-(7)/(5)+(8)/(5)=(1)/(5)`

Common difference =
`(1)/(5)`.

Hence the common difference of the arithmetic sequence is
`(1)/(5)`.