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Which term of the series \( \sqrt{2}, \dfrac{2}{3}, \dfrac{2 \sqrt{2}}{9},… \) is \( \dfrac{16}{2187} \)?
Let \( S_k \) be sum of an infinite \( \text{GP} \) whose first term is \( k \) and common ratio is \( \dfrac{k}{(k+1)}(k >0) \). Then the value of \( \sum_{k=1}^{\infty}\frac{(1)^k}{S_k} \) is equal to_______
The first term of an \( \text{AP} \) is \( a \) and the sum of the first \( p \) terms is zero, then the sum of its next \( q \) terms is ________
Let common difference of is .
Sum of next terms:
A man saved \( ₹66000 \) in 20 yrs. In such succeeding years after the first year, he saved \( ₹200 \) more than what he saved in the previous year. How much did he save in the first year?
First term yr.
Hence, he saved in the first year.
A man accepts a position with an initial salary of \( ₹5200 \) per month. It is understood that he will receive an automatic increase of \( ₹320 \) in the very next month and each month thereafter. What is his salary for the tenth month?
First term , Common difference
Salary for tenth month, for
A Carpenter was hired to build \( 192 \) window frames. The first day he made five frames and each day, threafter he made two more frames than he made the day before. How many days did it take him to finish the job?
Here and
Then
Find the sum of the series \( (3^32^3)+(5^34^3)+(7^36^3)+\ … \) to \( n \) terms _______
Given,
Find the \( r^{th} \) term of an \( \text{AP} \), where sum of whose first \( n \) terms is \( 2n+3n^2 \)______
term
If \( A \) is the \( \text{A.M} \) and \( G_1,\ G_2 \) be two \( \text{GM} \) between any two numbers, then find \( \dfrac{G_1^2}{G_2}+\dfrac{G_2^2}{G_1} \).
be between and , then are in
Let be the common ratio.
Then,
If the sum of \( n \) terms of an \( \text{AP} \) is given by \( S_n=3n+2n^2, \) then the common difference of the AP is_______
First term of the
and
Common difference
If \( 9 \) times the \( 9^{th} \) term of an \(\text{ AP} \) is equal to \( 13 \) times the \( 13^{th} \) term, then the \( 22^{nd} \) term of the \( \text{AP} \) is_______
If \( x,\ 2y, \) and \( 3z \) are in \( \text{AP} \) where the distinct numbers \( x,\ y, \) and \( z \) are in \( \text{GP} \), then the common ratio of the \( \text{GP} \) is__________
are in
—(1)
are in
From (1)
If in an \( \text{AP},\ S_n=qn^2 \) and \( S_m=qm^2, \) where \( Sr \) donates the sum of \( r \) terms of the \( \text{AP} \) then \( Sq \) equals to________
Now,
So, the series is
Here
The minimum value of \( 4^x+4^{1x}, x\in R \) is_______
minimum value of is
If \( Tn \) donates the \( n^{th} \) term of the series \( 2+3+6+11+18+… \ , \) then \( T_{50} \) is _______
If \( a,\ b, \) and \( c \) are in \( \text{GP} \) then the value of \( \dfrac{ab}{bc} \) is equal to______
(Since ) and are in )
The series \( 4,\ 1,\ \dfrac{1}{4},\ \dfrac{1}{16} \) are in ______
It is an
The series \( 13,\ 8,\ 3,\ 2,\ 7 \) are in_____
Here
It is an
If \( a^2,\ b^2,\ c^2 \) are in \( \text{AP} \) which of the following is also an \(\text{ AP} \)?
[Taking mathjax] ]
are an AP.
If the \( AM \) of \( a \) and \( b \) is \( \dfrac{a^n+b^n}{a^{n1}+b^{n1}} \), then the value of \( n \) is _______
\( \sum_{r=1}^{\infty} \dfrac{1+a+a^2+…+a^{r1}}{r!} \) is equal to_______
If \( \left\{ a_n \right\} \) is in \( \text{GP{ \) such that \( \dfrac{a_4}{a_6}=\dfrac{1}{4} \) and \( a_2+a_5=216 \), then \( a_1 \) is equal to______
when
The value of \( x \) which satisfies \( 1+\cos x+\cos^2x+…=64 \) in \( \left[\pi,\pi\right] \) is_______
If \( S \) is the sum, \( P \) is the product and \( R \) is the sum of the reciprocals of \( n \) terms of a \( GP \), then \( P^2 \) is equal to ______
If \( a_1,\ a_2,\ …\ a_{50} \) are in \(\text{ GP} \), then \( \dfrac{a_11_3+a_5…+a_{49}}{a_2a_4+a_6…+a_{50}} \) is equal to _______
(Say)