Question:
Which term of the following sequences:

$2 comma space 2 square root of 2 comma 4 comma space...$

Answer:

(a) The given sequence is $2 comma space 2 square root of 2 comma 4 comma space...$

Here, a = 2 and r = $fraction numerator 2 square root of 2 over denominator 2 end fraction equals square root of 2$

Let the nth term of the given sequence be 128.

$a subscript n space end subscript equals space a r to the power of n minus 1 end exponent rightwards double arrow open parentheses 2 close parentheses open parentheses square root of 2 close parentheses to the power of n minus 1 end exponent space equals space 128 rightwards double arrow open parentheses 2 close parentheses open parentheses 2 close parentheses to the power of fraction numerator n minus 1 over denominator 2 end fraction end exponent equals open parentheses 2 close parentheses to the power of 7 rightwards double arrow open parentheses 2 close parentheses to the power of fraction numerator n minus 1 over denominator 2 end fraction plus 1 end exponent equals open parentheses 2 close parentheses to the power of 7 s o space fraction numerator n minus 1 over denominator 2 end fraction plus 1 equals 7 rightwards double arrow fraction numerator n minus 1 over denominator 2 end fraction space equals space 6 rightwards double arrow n space minus 1 space equals space 12 rightwards double arrow n equals 13$

Thus, the 13th term of the given sequence is 128.

(b) The given sequence is $square root of 3 space comma space 3 comma space 3 square root of 3 space comma space... space i s space 729 ?$

Here, a= $square root of 3 space a n d space r space equals space fraction numerator 3 over denominator square root of 3 end fraction space equals space square root of 3$

Let the nth term of the given sequence be 729.

$a subscript n equals a r to the power of n minus 1 end exponent s o a r to the power of n minus 1 end exponent space equals space 729 rightwards double arrow open parentheses square root of 3 close parentheses space open parentheses square root of 3 close parentheses to the power of n minus 1 end exponent space equals space 729 rightwards double arrow open parentheses 3 close parentheses to the power of 1 half end exponent open parentheses 3 close parentheses to the power of fraction numerator n minus 1 over denominator 2 end fraction end exponent equals open parentheses 3 close parentheses to the power of 6 rightwards double arrow open parentheses 3 close parentheses to the power of 1 half plus fraction numerator n minus 1 over denominator 2 end fraction end exponent equals open parentheses 3 close parentheses to the power of 6 s o 1 half plus fraction numerator n minus 1 over denominator 2 end fraction equals 6 rightwards double arrow fraction numerator 1 plus n minus 1 over denominator 2 end fraction equals 6 rightwards double arrow n equals 12$

Thus, the 12th term of the given sequence is 729.

(c) The given sequence is $1 third comma space 1 over 9 comma space 1 over 27 comma space... space$

Here,

a= $1 third space space a n d space r space equals space 1 over 9 obelus divided by 1 third equals 1 third$

Let the nth term of the given sequence be $1 over 19683$ .

$a subscript n space equals space a r to the power of n minus 1 end exponent s o a r to the power of n minus 1 end exponent equals 1 over 19683 rightwards double arrow open parentheses 1 third close parentheses open parentheses 1 third close parentheses to the power of n minus 1 end exponent equals 1 over 19683 rightwards double arrow open parentheses 1 third close parentheses to the power of n equals open parentheses 1 third close parentheses to the power of 9 rightwards double arrow n equals 9$

Thus, the 9th term of the given sequence is $1 over 19683$ .

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Question:
Which term of the following sequences:

$2 comma space 2 square root of 2 comma 4 comma space...$

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Question: Which term of the following sequences:

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Question:
Which term of the following sequences:

$2 comma space 2 square root of 2 comma 4 comma space...$