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What is the 21st term in the following geometric sequence? –8, 16, –32, 64, –128,

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2 Answers

-8, 16, –32, 64, –128 
 
This corresponds to the following form of sequence:
a X (-2n-1), being a = 8 and r ( common ratio) = -2
then the 21 term will be
a X r(21-1)= 8 x (-2)20 = -8388608
 
The terms in the sequence are:
 
-2n-1*8,  n=1,2,3,...      (Since 8=23,we could also write the sequence as -2n+2, n=1,2,3,...)
 
The 21st term occurs for n=21:
 
-221-1*8 = -220*8
 
Use your calculator to compute the answer.