Write the first five terms of the geometric sequence a_1=7,a_(k+1)=2a_k and determine the common ratio and write the nth term of the sequence as a function of n

Winston Todd

Winston Todd

Answered question

2022-10-17

Write the first five terms of the geometric sequence a 1 = 7 , a k + 1 = 2 a k and determine the common ratio and write the nth term of the sequence as a function of n

Answer & Explanation

Bridget Acevedo

Bridget Acevedo

Beginner2022-10-18Added 19 answers

Given the first term, a 1 = 7 and the recursive formula for the geometric sequence, a k + 1 = 2 a k , we know the common ratio must be 2, since the recursive formula multiplies 2 to the k t h term to get the ( k + 1 ) t h term.

Since we know the common ratio is 2 and the first term is 7, we can write our explicit formula for the geometric sequence using the general form:
a n = a 1 ( r n - 1 )

By substituting our known values, we get:
a n = 7 ( 2 n - 1 ) which allows us to find the nth term as a function of n

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