How do you write the first five terms of the sequence defined recursively a_1=14,a_(k+1)=(−2)a_k, then how do you write the nth term of the sequence as a function of n?

Dymnembalmese2n 2022-09-22 Answered
How do you write the first five terms of the sequence defined recursively a 1 = 14 , a k + 1 = ( - 2 ) a k , then how do you write the nth term of the sequence as a function of n?
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Answers (1)

Carina Moon
Answered 2022-09-23 Author has 6 answers
We are given a 1 = 14 and as a k + 1 = ( - 2 ) a k , we have
a 2 = ( - 2 ) a 1 = ( - 2 ) × 14 = - 28
a 3 = ( - 2 ) a 2 = ( - 2 ) × ( - 28 ) = 56
a 4 = ( - 2 ) × a 3 = ( - 2 ) × ( 56 = - 112 and
a 5 = ( - 2 ) × ( - 112 ) = 224
It is apparent that it is geometric sequence with first term a 1 = 14 and common ratio as −2. As such n t h term a n is given by
a n = a 1 × ( - 2 ) ( n - 1 ) = 14 ( - 2 ) ( n - 1 )
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