Question

-17/4 is the ____ term of 2 1/4, 2, 1 3/4, .....?

Answer 1

`-(17)/(4)` is 27th term of the given sequence.

Explanation:

Given sequence is
`2(1)/(4),2,1(3)/(4),......`

Here, first term of the sequence,

`a_1=2(1)/(4)`

By subtracting first term from the second term of the sequence,

`T_2-T_1=2-2(1)/(4)`

=
`(2-2)-(1)/(4)`

=
`-(1)/(4)`

Similarly, difference in second and third term,

`1(3)/(4)-2=(1-2)+(3)/(4)`

=
`-1+(3)/(4)`

=
`(3-4)/(4)`

=
`-(1)/(4)`

Therefore, there is a common difference (d) of
`(-(1)/(4))`.

Hence, the sequence is an Arithmetic sequence.

Explicit formula of an Arithmetic sequence is given by,

`T_n=a_1+(n-1)d`

Here, n = number of term

If,
`T_n=-(17)/(4)`

By substituting these values in the formula,

`-(17)/(4)=2(1)/(4)+(n-1)(-(1)/(4))`

`-(17)/(4)-2(1)/(4)=(n-1)(-(1)/(4))`

`-(17)/(4)-(9)/(4)=-(n-1)((1)/(4))`

`-((17+9)/(4))=(n-1)((1)/(4))`

`(26)/(4)=(1)/(4)(n-1)`

n - 1 = 26

n = 27

Therefore,
`-(17)/(4)` is 27th term of the given sequence.