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Geometric Sequences - Questions

Question 1
124507

If \(x, y, z\) are consecutive terms in a geometric series, \(x+y+z=13\), and \(x y z=27\), then \(x+z=\)

A.

15

B.

12

C.

10

D.

8

10

Question 2
12005

The 10th term of the geometric sequence 2, 4, 8, ... is?

1024

Question 3
12006

Find the common ratio, given that it is negative, of a G.P. whose first term is 8 and whose fifth term is \(\dfrac{1}{2}\)

\( - \dfrac{1}{2}\)

Question 4
12007

The 9th term of the G.P. 3, -6, 12, ... is?

768

Question 5
12008

The 6th term of a G.P. is 16 and the 3rd term is 2. The first term is?

\(\dfrac{1}{2}\)

Question 6
12009

The 3rd term of a G.P. is 2 and the 5th term is 18. The common ratio is?

\( \pm 3\)

Question 7
11985

The 12th term of the geometric sequence -2, 4, -8, ... is

4096

Question 8
11986

The third term of a geometric sequence is \(\dfrac{3}{4}\) and the seventh term is 12. The fifth term is?

\({{\rm{T}}_5} = 3\)

Question 9
24650

A geometric series has a second term 4.5 and the ratio of the fourth term to the third term is 1.5.

(i)  Find the common ratio \(r\)

(ii)  What is the first term \(a\)?

(iii)  Calculate the sum of the first 9 terms.

(i)  1.5

(ii)  the first term is 3

(iii)  \({S_9} = 224\dfrac{{169}}{{256}}\)

Question 10
24651

Find the number which when added to 3, 7 and 14 will give a set of numbers in geometric progression.

\(k = 2\dfrac{1}{3}\)

Question 11
24652

The 6th term of a geometric progression is 16 and the 3rd term is 2.

(i)  Find the common ratio.

(ii)  Find the first term.

(i)  \(r = 2\)

(ii)  \(a = \dfrac{1}{2}\)

Question 12
24653

In a geometric sequence the eighth term is 384 and the third term is 12, find

(i)  Find the common ratio.

(ii)  Find the first term.

(i)  \(r = 2\)

(ii)  \(a = 3\)

Question 13
25869

How many terms of the geometric series, \(4 + 2 + 1 + \ldots \) must be added to obtain a sum of \(7\dfrac{{15}}{{16}}\)?

\(n=7\)