APs and GPs

The common ratio of the geometric sequence 8, 12, 18, ... is

• $\frac{3}{4}$

• $\frac{2}{3}$

• $\frac{3}{2}$

• $\frac{1}{2}$

Which of the following is NOT an arithmetic sequence?

• 11, 2, -8, -19, ...

• 8, 12, 16, 20, ...

• 51, 45, 39, 33,

• -7, -9, -11, -13, ...

For the arithmetic progression -12, -7, -2, 3, 8, ..., the nth term is given by

• $5n-17$

• $5n-12$

• $-12-5n$

• $5n+17$

In a geometric progression, each of whose terms is positive, the fifth term is 45 and the seventh term is 5. The SIXTH term is

• 9

• 15

• 25

• 40

The sum of first 10 terms of the sequence 2, -1, -4 is

• -170

• -125

• -115

• -85

The sequence of positive integers  $\left\{t_n\right\}$   is defined by  $t_n=3\left(\frac{1}{2}\right)^{\left(n-1\right)}$  .  The 10th term of the sequence is given by 

•  $\frac{19683}{512}$  

•  $\frac{3}{256}$  

•  $\frac{3}{512}$  

•  $\frac{3}{1000}$  

3 is the geometric mean of a and b. The value of a and b are

• 2 and 4

• 4 and 5

• 1 and 9

• 0 and 9

The sum of the ODD integers between 10 and 50 is

• 60

• 600

• 630

• 1960

The sum of the first n terms of a geometric series is given by  $S_n=4^n-1$  .    For this series

I.    The common ratio is 4
II.   The first 3 terms are 3, 15 and 63
III.   $S_{2n}=2^{4n}-1$  

Which of the above statements are correct?

• I and II only

• I and III only

• II and III only

• I, II and III

A long distance runner runs the first kilometre of a race in 3 minutes 45 seconds but finds that his speed drops steadily so that each kilometre takes him 12 seconds more than the preceding one. The time taken to cover the first 12 kilometres is

• 58 mins 12 secs

• 31 mins 48 secs

• 9 mins 18 secs

• 63 mins 36 secs