What is the 10th term of this geometric sequence 1, 2, 4, 8, …?

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Answer 1 · 2015-08-10T06:55:28

$color(blue)(T_10= 512$

the geometric sequence given is:
$1 , 2 , 4, 8$ ...

When provided with a geometric sequence we must first calculate the common ratio $r$

$r$ is obtained by dividing a term by its preceding term:

1) $2/1 =2$

2) $4/2 =2$

for this sequence the common ratio $r = 2$ the first term $a = 1$

The 10th term can be obtained through formula:

$color(blue)(T_n = ar^(n-1)) = 1 xx 2^((10-1))$ , where $n$ = 10

$T_10= 1 xx 2^9$

$color(blue)(T_10= 1 xx 512= 512$