Which term of the sequence { 16/9, 4/3, 1, 3/4 ... } is 243/1024

Emilio Calhoun

Emilio Calhoun

Answered question

2022-10-13

Which term of the sequence { 16/9, 4/3, 1, 3/4 ... } is 243/1024

Answer & Explanation

Annabella Ferguson

Annabella Ferguson

Beginner2022-10-14Added 15 answers

This is a geometric sequence with initial term 16 9 and common ratio 3 4 .
The general term of the sequence can be written:
a n = 16 9 ( 3 4 ) n - 1 = ( 3 4 ) n - 3 for n=1,2,3,...
Observe that 243 = 3 5 and 1024 = 2 10 = 4 5
Comparing this power with the expression n−3, we find that:
a 8 = 243 1024

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