Find the nth term:

Question:

[tex]\large\frac{8}{101} , \frac{9}{91} , \frac{10}{81} , \frac{11}{71} \\[/tex]

Answer:

[tex]\large\frac{8}{101} , \frac{9}{91} , \frac{10}{81} , \frac{11}{71},\boxed{\frac{12}{61},\frac{13}{51},\frac{14}{41},\frac{15}{31},\frac{16}{21},\frac{17}{11}}\\[/tex]

Solution:

For the numerator, we will add 1, and for the denominator, we will subtract it by 10.

#staysmart;)

Verified answer

Answer:

[tex]\large\boxed{ \sf{ \pmb{\frac{12}{61}}}}[/tex]

Step-by-step explanation:

Given that,

[tex]\large \sf {\frac{8}{101} , \frac{9}{91} , \frac{10}{81} , \frac{11}{71} ... } \\[/tex]

To Find:

nth term

Solution:

We have to add 1 in numerator and -10 in denominator.

[tex] \implies\sf\large\frac{8}{101} , \frac{9}{91} , \frac{10}{81} , \frac{11}{71} \sf \: \: \: \pmb{[Given]} \\ [/tex]

[tex]\:[/tex]

[tex] \implies\sf\large \frac{8 + 1}{101 - 10} = \frac{9}{91} \\ [/tex]

[tex]\:[/tex]

[tex] \implies\sf \large \frac{9 + 1}{91 - 10} = \frac{10}{81} \\ [/tex]

[tex]\:[/tex]

[tex]\implies\sf \large \frac{10 + 1}{81 - 10} = \frac{11}{71} \\ [/tex]

[tex]\:[/tex]

[tex]\implies\sf \large \frac{11 + 1}{71 - 10} = \frac{12}{61} ... \\ [/tex]

The difference is 1 in numerator so we add 1 and the difference is -10 in denominator so we subtract -10.