Question

❤️100 points❤️✌️✌️
❤️❤️Solve this if u can .
With explanation ..❤️❤️

❎❎no spam plzz❎❎​

Answer 1

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$


$\underline{ \bf{Given :}}$

$a_{n} \: = \: 666666666... \: n \: times$


$\underline{ \bf{To \: Find : a_{n} \: \: }}$


$\underline{ \bf{Correct \: Answer : }} \: \: \boxed{ \: (i) \: \frac{6( {10}^{n} - 1) \: }{9} }$


$\underline{ \bf{Explanation :}}$


$a_{n} \: = \: 666666666... \: n \: times$

We can write it in this way also,
$a_{n} \: = \: 6 \times {10}^{0} + 6 \times {10}^{1} + 6 \times {10}^{2} + ... \: 6 \times {10}^{n - 1}$


Taking 6 as common,

$a_{n} \: = \: 6(1 \times {10}^{0} + 1 \times {10}^{1} + 1 \times {10}^{2} + ... \: 1 \times {10}^{n - 1} )$

$a_{n} \: = \: 6(1 + {10}^{1} + {10}^{2} + ... {10}^{n - 1} )$

As we can see it is in the form of G.P ,
So by using the formula of Sum of all terms of G.P we get,

$a _{n} = 6 \: [\frac{a( {r}^{n} - 1) }{r - 1} ]$

$a _{n} = 6 \: [\frac{1( {10}^{n} - 1) }{10 - 1} ]$

$a_{n} = \: \frac{6( {10}^{n} - 1) }{9}$


Hence, the correct answer is (a).

Answer 2

Hey dear ‼️

Answer....

plzz refer to the attached file....

keep loving...❤️❤️❤️❤️☺️