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Variation of G Due to Height and Depth

Values of '...

Question

Values of $^{'} n^{'}$ and $c$ are such that:
$(i) n \sum n = 1 r, \frac{\sqrt{10}}{3} n \sum n = 1 r^{2}, n \sum r = 1 r^{3}$ are in increasing G.P.
Find the value of $n$ .

A

4

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B

6

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C

16

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D

36

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Solution

The correct option is A 4

Hence, the value of $n$ is $4$ .

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Similar questions

Q. The value of

n \sum r = 1 r \times r!

n

natural numbers we have the following results with usual notations

n \sum r = 1 r = \frac{n (n + 1)}{2}, n \sum r = 1 r^{2} = \frac{n (n + 1) (2 n + 1)}{6}, n \sum r = 1 r^{3} = {(n \sum r = 1 r)}^{2}

a_{1} a_{2} . . . . a_{n} \in A . P

n

terms of the sequence

\frac{1}{a_{1} a_{2}}, \frac{1}{a_{2} a_{3}}, . . . \frac{1}{a_{n - 1} a_{n}}

\frac{n - 1}{a_{1} a_{n}}

n

G . P

with first term '

a

' & common ratio '

r

S_{n} = \frac{l r - a}{r - 1}

r \neq 1

r = 1

n

G . P .

n

a

, where the sum to infinite terms of

G . P .

is the limiting value of

\frac{l r - a}{r - 1}

n \to \infty, | r | < l

l

is the last term of

G . P .

On the basis of above data answer the following questionsThe sum of the series

\frac{1}{2.3} + \frac{1}{3.4} + . . .

n

x_{1}, x_{2}, x_{3}, \dots, x_{n}

are n-values of a variable x such that

\sum_{i = 1}^{n} u_{i} = 90

\sum_{i = 1}^{n} V_{i} = 150

u_{i} = 2 x_{i} - 3

V_{i} = 3 x_{i} - 4

, for i = 1, 2, 3, 4, …, n, then the value of n will be

Q. A and b are two sets such that

n (A) = 3

n (B) = 6

.
Find (i) minimum value of

n (A \cup B)

(ii) maximum value of

n (A \cup B)

x_{1}, x_{2}, . . . . . x_{n}

n

values of a variable

X

y_{1}, y_{2}, . . . . . y_{n}

n

values of a variable

Y

y_{i} = \frac{x_{i} - a}{h}; i = 1, 2, . . . . ., n

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