Question

Q.19
The tenth term of the geometric sequence
1/4,- 1/2
, 1, -2, ... is -

A) 1024 B)
1
1024
C) -128 D)
--1
128​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The tenth term of the geometric sequence

1/4,- 1/2 , 1, -2, ... is

A) 1024

B) 1/1024

C) -128

D) - 1/128

EVALUATION

Here the given geometric sequence is

1/4,- 1/2 , 1, -2, ...

First term = a = 1/4

Common Ratio = r = - 2 ( < 1 )

Hence the required tenth term of the geometric sequence

$\displaystyle\sf{ = a \times {r}^{n - 1} }$

$\displaystyle\sf{ = \frac{1}{4} \times {( -2 )}^{10 - 1} }$

$\displaystyle\sf{ = \frac{1}{4} \times {( -2 )}^{9} }$

$\displaystyle\sf{ = \frac{1}{4} \times ( -512 ) }$

$\displaystyle\sf{ = - 128 }$

FINAL ANSWER

Hence the correct option is C) - 128

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