How about we expect x to be the quantity of days in which 150 laborers finish the work. Then, at that point, from the inquiry, we have \[\mathbf{150x}\text{ }=\text{ }\mathbf{150}\text{ }+\text{...
Given, the expense of machine \[=\text{ }\mathbf{Rs}\text{ }\mathbf{15625}\] Additionally, considering that the machine deteriorates by 20% consistently. Consequently, its worth after consistently...
Given, the man saved Rs 10000 in a bank at the pace of 5% basic premium yearly. Subsequently, the interest in first year \[=\text{ }\left( \mathbf{5}/\mathbf{100} \right)\text{ }\mathbf{x}\text{...
It's seen that, The quantities of letters sent structures a \[\mathbf{G}.\mathbf{P}.:\text{ }\mathbf{4},\text{ }\mathbf{42},\text{ }\ldots \text{ }\mathbf{48}\] Here, \[\mathbf{initial}\text{...
Given, Shamshad Ali purchases a bike for Rs 22000 and pays Rs 4000 in real money. Thus, the neglected sum \[=\text{ }\mathbf{Rs}\text{ }\mathbf{22000}\text{ }\text{ }\mathbf{Rs}\text{...
Given, the rancher pays Rs 6000 in real money. In this way, the neglected sum \[=\text{ }\mathbf{Rs}\text{ }\mathbf{12000}\text{ }\text{ }\mathbf{Rs}\text{ }\mathbf{6000}\text{ }=\text{...
nth term of the numerator \[=~n{{\left( n~+\text{ }1 \right)}^{2}}~\] \[=~{{n}^{3}}~+\text{ }2{{n}^{2}}~+\text{ }n\] and the nth term of the denominator \[=~{{n}^{2}}\left( n~+\text{ }1 \right)\]...
solution:
As the question says, we have In this way, from (1) and (2), we have \[\mathbf{9S22}\text{ }=\text{ }\mathbf{S3}\text{ }\left( \mathbf{1}\text{ }+\text{ }\mathbf{8S1} \right).\]
The given series is \[\mathbf{3}\text{ }+\text{ }\mathbf{7}\text{ }+\text{ }\mathbf{13}\text{ }+\text{ }\mathbf{21}\text{ }+\text{ }\mathbf{31}\text{ }+\text{ }\ldots \] \[\mathbf{S}\text{ }=\text{...
Given series is \[\mathbf{2}\text{ }\times \text{ }\mathbf{4}\text{ }+\text{ }\mathbf{4}\text{ }\times \text{ }\mathbf{6}\text{ }+\text{ }\mathbf{6}\text{ }\times \text{ }\mathbf{8}\text{ }+\text{...
(i) Given, \[\mathbf{5}\text{ }+\text{ }\mathbf{55}\text{ }+\text{ }\mathbf{555}\text{ }+\text{ }\ldots \] Let \[\mathbf{Sn}\text{ }=\text{ }\mathbf{5}\text{ }+\text{ }\mathbf{55}\text{ }+\text{...
Given a, b, c are in A.P. Thus, \[\mathbf{b}\text{ }\text{ }\mathbf{a}\text{ }=\text{ }\mathbf{c}\text{ }\text{ }\mathbf{b}\text{ }\ldots \text{ }\left( \mathbf{1} \right)\] What's more,...
Leave the two numbers alone an and b. \[A.M\text{ }=\text{ }\left( a\text{ }+\text{ }b \right)/2\text{ }and\text{ }G.M.\text{ }=\text{ }\surd ab\] From the inquiry, we have
Given, an and b are the foundations of \[\mathbf{x2}\text{ }\text{ }\mathbf{3x}\text{ }+\text{ }\mathbf{p}\text{ }=\text{ }\mathbf{0}\] Along these lines, we have \[\mathbf{a}\text{ }+\text{...
Given, a, b, c,and d are in G.P. Along these lines, we have \[\therefore \mathbf{b2}\text{ }=\text{ }\mathbf{ac}\text{ }\ldots \text{ }\left( \mathbf{I} \right)\] \[\mathbf{c2}\text{ }=\text{...
If are in A.P
We should expect t and d to be the initial term and the normal distinction of the A.P. individually. Then, at that point, the nth term of the A.P. is given by, \[\mathbf{a}\text{ }=\text{...
![\[{{\mathbf{P}}^{\mathbf{2}}}{{\mathbf{R}}^{n}}^{~}=\text{ }{{\mathbf{S}}^{n}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8f2aab769c8cb513e5ed7cf5988b4ab7_l3.png "Rendered by QuickLaTeX.com")
Give the terms access G.P. be \[\mathbf{a},\text{ }\mathbf{ar},\text{ }\mathbf{ar2},\text{ }\mathbf{ar3},\text{ }\ldots \text{ }\mathbf{arn}\text{ }\text{ }\mathbf{1}\ldots \] Structure the inquiry,...
Given, On cross duplicating, we have Likewise, given On cross duplicating, we have From (1) and (2), we get \[\mathbf{b}/\mathbf{a}\text{ }=\text{ }\mathbf{c}/\mathbf{b}\text{ }=\text{...
How about we think about the terms in A.P. to be \[\mathbf{a},\text{ }\mathbf{a}\text{ }+\text{ }\mathbf{d},\text{ }\mathbf{a}\text{ }+\text{ }\mathbf{2d},\text{ }\mathbf{a}\text{ }+\text{...
We should consider the terms in the G.P.to be \[\mathbf{T1},\text{ }\mathbf{T2},\text{ }\mathbf{T3},\text{ }\mathbf{T4},\text{ }\ldots \text{ }\mathbf{T2n}.\] The quantity of terms \[=\text{...
How about we think about the three numbers in G.P. to be as \[\mathbf{a},\text{ }\mathbf{ar},\text{ }\mathbf{and}\text{ }\mathbf{ar2}.\] Then, at that point, from the inquiry, we have...
How about we consider an and r to be the initial term and the normal proportion of the G.P. separately. Given, \[\mathbf{a}\text{ }=\text{ }\mathbf{1}\] \[\mathbf{a3}\text{ }=\text{...
Considering that the amount of certain terms in a G.P is \[\mathbf{315}.\] Leave the quantity of terms alone n. We realize that, amount of terms is Considering that the initial term an is...
Considering that, \[\mathbf{f}\text{ }\left( \mathbf{x}\text{ }+\text{ }\mathbf{y} \right)\text{ }=\text{ }\mathbf{f}\text{ }\left( \mathbf{x} \right)\text{ }\times \text{ }\mathbf{f}\text{ }\left(...
We need to initially track down the two-digit numbers, which when partitioned by 4, yield 1 as remaining portion. They are: \[\mathbf{13},\text{ }\mathbf{17},\text{ }\ldots \text{...
First how about we discover the whole numbers from\[\mathbf{1}\text{ }\mathbf{to}\text{ }\mathbf{100}\] , which are distinguishable by 2. What's more, they are\[\mathbf{2},\text{ }\mathbf{4},\text{...
First how about we discover the numbers somewhere in the range of \[\mathbf{200}\text{ }\mathbf{and}\text{ }\mathbf{400}\] which are detachable by \[\mathbf{7}.\] The numbers are:...
We should take an and d to be the initial term and the normal distinction of the A.P. individually. Thus, we have
We should think about the three numbers in A.P. as \[\mathbf{a}\text{ }\text{ }\mathbf{d},\text{ }\mathbf{a},\text{ }\mathbf{and}\text{ }\mathbf{a}\text{ }+\text{ }\mathbf{d}.\] Then, at that point,...
How about we take an and d to be the initial term and the normal distinction of the A.P. individually. We realize that, the kth term of A. P. is given by \[\mathbf{ak}\text{ }=\text{...