Q

#### Geometric progression

(10 Questions)The geometric series are introduced in this lesson, as well as n'th term.

0

1

The first term of a geometric sequence is 192 and the fifth term is 0.75. What is the common ratio?

**A**

**B**

**C**

**D**

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1

The fourth term of a geometric sequence is 27 and the seventh term is 1. What is the first term?
Enter your answer as an integer.

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1

The first term of a geometric sequence is 5 and the sixth term is 160. What is the common ratio?
Enter your answer as an integer.

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1

Is it a geometric sequence? If it is, find the first term and the common ratio"
-\frac{1}{2}, \frac{1}{4}, -\frac{1}{8}, \frac{1} {16}, ......

**A**

**B**

**C**

**D**

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1

Given the terms a_{10} = \frac{3}{512} and a_{15} = \frac{3}{16384} of a geometric sequence, find the exact value of the term a_{30} of the sequence.

**A**

**B**

**C**

**D**

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1

Find the 10 th term of a geometric sequence if a_1 = 45 and the common ratio r = 0.2.

**A**

**B**

**C**

**D**

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1

The n-th term of a geometric sequence with initial value a and common ratio r is given by
a_{n} = ar^{n-1}
What is the ninth term of the geometric sequence 81, 27, 9, 3, ...?

**A**

**B**

**C**

**D**

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1

Match the following series
\text { A) Infinite series } 1) a, ar, ar^2...........ar^{n-1}
\text{ B) Finite series } 2) a, ar, ar^2 .......

**A**

**B**

**C**

**D**

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1

The general form of a geometric sequence is
a, ar, ar^{2}, ar^{3}, ar^{4}.......
Find the terms a_2, a_3, a_4 \text{ and } a_5 of a geometric sequence if a_1 = 10 and the common ratio r = - 1.

**A**

**B**

**C**

**D**

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1

Geometric sequence (geometric progression):
It is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.
The common ratio (r) is obtained by dividing any term by the preceding term.
r = \frac{a_2}{a_1} = \frac{a_3}{a_2}........= \frac{a_n}{a_{n-1}}
where r = common ratio
a_1 = first term,
a_2 = second term,
a_3 = third term
a_{n-1} = the term before the n th term
a_n = the n th term
Which of the following is in geometric progression
A) 10, 30, 90, 270, 810,.......
B) 1, 2, 4, 8, 16, 32...........

**A**

**B**

**C**

**D**

by Krishna