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Standard XII

Mathematics

Common Ratio

The sequence ...

Question

The sequence $- 6 + 42 - 294 + 2058$ is a

finite geometric sequence

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finite arithmetic sequence

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infinite geometric sequence

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infinite harmonic sequence

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Solution

The correct option is A finite geometric sequence
The sequence $- 6 + 42 - 294 + 2058$ is a finite geometric sequence.
Here the common ratio is $- 7$ .
As it has finite terms, therefore the series is finite sequence.

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Similar questions

Q. Suppose the sequence

a_{1}, a_{2}, a_{3} . . . . .

is an arithmetic progression of distinct numbers such that the

a_{1}, a_{2}, a_{4}, a_{6} . . . . .

is a geometric progression. The common ration of the geometric progression is:

There are

4 n + 1

terms in a sequence of which first

2 n + 1

are in Arithmetic Progression and last

2 n + 1

are in Geometric Progression in which the common difference of Arithmetic Progression is

2

and common ratio of Geometric Progression is

\frac{1}{2}

. The middle term of the Arithmetic Progression is equal to middle term of Geometric Progression. Let middle term of the sequence is

T_{m}

and

T_{m}

is the sum of infinite Geometric Progression whose sum of first Two terms is

{(\frac{5}{4})}^{2} n

and ratio of these terms is

\frac{9}{16}

First term of given sequence is equal to

Q. The first three terms of geometric sequence are

x, y, z

and these have the sum equal to

42

. If the middle term

y

is multiplied by

5 / 4

, the number

x

\frac{5 y}{4}

z

now form an arithmetic sequence . The largest possible value of

x

, is

I want all formulas related to sequence and series

That is related to Harmonic progression , AritmArith progression , Geometric progression and special progression

Q. The arithmetic mean of two numbers is

\frac{13}{2}

and their geometric mean is

6

. Find their harmonic mean.

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The sequence −6+42−294+2058 is a

The correct option is A finite geometric sequenceThe sequence −6+42−294+2058 is a finite geometric sequence.Here the common ratio is −7.As it has finite terms, therefore the series is finite sequence.

The sequence $- 6 + 42 - 294 + 2058$ is a

The correct option is A finite geometric sequence
The sequence $- 6 + 42 - 294 + 2058$ is a finite geometric sequence.
Here the common ratio is $- 7$ .
As it has finite terms, therefore the series is finite sequence.