Write the first five terms of the geometric sequence a_1=5,a_(k+1)=−2a_k and determine the common ratio and write the nth term of the sequence as a function of n

Jaelyn Payne 2022-10-11 Answered
Write the first five terms of the geometric sequence a 1 = 5 , a k + 1 = - 2 a k and determine the common ratio and write the nth term of the sequence as a function of n
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Answers (1)

Bobby Mcconnell
Answered 2022-10-12 Author has 8 answers
a 1 = 5 and a k + 1 = - 2 a k
so, a 2 = - 2 a 1
=> a 2 = - 10
Also, a 3 = - 2 a 2
i.e. a 3 = 20
so, our terms are 5,−10,20,−40,...
Hence, 1st term 5 and common ratio -2
Now, nth term is a r n - 1
i.e. 5 ( - 2 ) n - 1 )
or, ( - 5 2 ) ( - 2 n )
With n = 7 we have:
( - 5 2 ) ( - 2 7 ) = 320
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