Question

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

Answer 1

Answer:

$-\frac{17}{4}$ is 27th term of the given sequence.

Step-by-step explanation:

Given sequence is $2\frac{1}{4},2,1\frac{3}{4},......$

Here, first term of the sequence,

$a_1=2\frac{1}{4}$

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

$T_2-T_1=2-2\frac{1}{4}$

            = $(2-2)-\frac{1}{4}$

            = $-\frac{1}{4}$

Similarly, difference in second and third term,

$1\frac{3}{4}-2=(1-2)+\frac{3}{4}$

           = $-1+\frac{3}{4}$

           = $\frac{3-4}{4}$

           = $-\frac{1}{4}$

Therefore, there is a common difference (d) of $(-\frac{1}{4})$.

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, $T_n=-\frac{17}{4}$

By substituting these values in the formula,

$-\frac{17}{4}=2\frac{1}{4}+(n-1)(-\frac{1}{4})$

$-\frac{17}{4}-2\frac{1}{4}=(n-1)(-\frac{1}{4})$

$-\frac{17}{4}-\frac{9}{4}=-(n-1)(\frac{1}{4})$

$-(\frac{17+9}{4})=(n-1)(\frac{1}{4})$

$\frac{26}{4}=\frac{1}{4}(n-1)$

n - 1 = 26

n = 27

Therefore, $-\frac{17}{4}$ is 27th term of the given sequence.