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

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 (A) 3 (B) 4 (C) 6 (D) 7

Tardigrade Admin · Accepted Answer

a >10 ....(1) ar 4< 1000 10 r 4< ar 4< 1000 r 4< 100 ⇒ r 2< 10 ∴ r ∈ -3,-2,-1,0,1,2,3 ⇒ 6 integral values. Note: 0 is rejected

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

3

4

6

7

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

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

3

4

6

7

a>10 ....(1) ar4<1000 10r4<ar4<1000 r4<100⇒r2<10 ∴r∈{−3,−2,−1,0,1,2,3}⇒6 integral values. Note: 0 is rejected

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