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#