Write a rule for the nth term of the geometric sequence and then find a_5 given a_4=−3,r=−2

Emmy Swanson

Emmy Swanson

Answered question

2022-10-14

Write a rule for the nth term of the geometric sequence and then find a 5 given a 4 = - 3 , r = - 2

Answer & Explanation

Mohammad Cantrell

Mohammad Cantrell

Beginner2022-10-15Added 10 answers

the terms in a standard geometric sequence are
a , a r , a r 2 , a r 3 , ... ... , a r n - 1
where a is the first term and r the common ratio
the nth term is
x a n = a r n - 1
a 4 = a r 3 = - 3 a = - 3 ( - 2 ) 3 = - 3 - 8 = 3 8
a n = 3 8 ( - 2 ) n - 1
a 5 = 3 8 ( - 2 ) 4 = 3 8 × 16 = 6

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