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Question

Consider the sequence a_n =5/7a_{n-1 , where}   a₁  =-3 7/12 to complete problems 19-21. Circle the most appropriate answers and fill in any applicable blanks. 

19. This sequence diverges/converges. If "converges," it converges to___. 

20. it has a common ratio/difference, whose absolute  value is less/greater than 1. 

21. the related series has a calculable sum/does not have a calculable sum. 

 

Answer 1

a_n and a_n-1 are consecutive values.  Dividing the current by the preceding value gives you the common ratio of 5/7.  Since this ratio is less than 1, the sequence converges 0.  The series has a calculable sum.