1. Tardigrade
  2. Question
  3. Mathematics
  4. The first term of a geometric sequence is greater than 10 and the fifth term is less than 1000. If r is the common ratio then the number of integral values of r, is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The first term of a geometric sequence is greater than 10 and the fifth term is less than 1000. If r is the common ratio then the number of integral values of r, is

Sequences and Series

Solution:

$ a >10$ ....(1)
$ar ^4< 1000$
$10 r ^4< ar ^4< 1000$
$r ^4< 100 \Rightarrow r ^2< 10$
$\therefore r \in\{-3,-2,-1,0,1,2,3\} \Rightarrow 6$ integral values.
Note: 0 is rejected