Determine whether the following sequence is geometric. If it is find the term and the common ratio. a_n=(-5)^(n-1) First term ? Common ratio ?

sumasintihg

sumasintihg

Answered question

2022-09-03

Determine whether the following sequence is geometric. If it is find the term and the common ratio.
a n = ( 5 ) n 1
First term ? Common ratio ?

Answer & Explanation

zoranovxp

zoranovxp

Beginner2022-09-04Added 7 answers

Solution : a n = ( 5 ) n 1
First term: a 1 = ( 5 ) 1 1 = ( 5 ) 0 = 1
Similarly, we find second term a 2 = ( 5 ) 2 1 = ( 5 ) 1 = 5
And third term a 3 = ( 5 ) 3 1 = ( 5 ) 2 = 25
We have ratios a 2 a 1 = 5 1 = 5
And a 3 a 2 = 25 ( 5 ) = 5
Since a 2 a 1 = a 3 a 1
Thus the sequence is a geometrical sequence.
We see that a 2 a 1 = a 3 a 2 = 5
Hence common ratio is -5.

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