It's perceived from the inquiry that, the points of the polygon will frame an A.P. with normal contrast \[d\text{ }=\text{ }5{}^\circ \text{ }and\text{ }initial\text{ }term\text{ }a\text{ }=\text{...
A man starts repaying a loan as first instalment of Rs. 100. If he increases the instalment by Rs 5 every month, what amount he will pay in the 30th instalment?
Given, The primary portion of the advance is \[Rs\text{ }100.\] The second portion of the credit is \[Rs\text{ }105,\]etc as the portion increments by \[Rs\text{ }5\]consistently. In this way, the...
Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)th numbers is 5: 9. Find the value of m.
How about we consider \[{{a}_{1}},\text{ }{{a}_{2}},\text{ }\ldots \text{ }{{a}_{m}}~be~m\]numbers to such an extent that \[1,\text{ }{{a}_{1}},\text{ }{{a}_{2}},\text{ }\ldots \text{...
If fig given below is the A.M. between a and b, then find the value of n.
Solution:- The A.M among \[a\text{ }and\text{ }b\]is given by, \[\left( a\text{ }+\text{ }b \right)/2\] Then, at that point, as indicated by the inquiry, Along these lines, the worth of \[n\text{...
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
We should expect\[{{A}_{1}},\text{ }{{A}_{2}},\text{ }{{A}_{3}},\text{ }{{A}_{4}},\text{ }and\text{ }{{A}_{5}}\] to be five numbers between \[8\text{ }and\text{ }26~\]with the end goal that...
If the sum of n terms of an A.P. is 3n^2 + 5n and its mth term is 164, find the value of m.
How about we take \[a\text{ }and\text{ }d\]to be the initial term and the normal contrast of the A.P. separately. \[{{a}_{m}}~=~a~+\text{ }(m~\text{ }1)d~=\text{ }164\text{ }\ldots \text{ }\left( 1...
The ratio of the sums of m and n terms of an A.P. is m^2: n^2. Show that the ratio of mth and nth term is (2m – 1): (2n – 1).
How about we take \[a\text{ }and\text{ }d\]to be the initial term and the normal contrast of the A.P. separately. Then, at that point, it given that Hence, the given result is proved.
Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that
Solution:- How about we take \[a\text{ }and\text{ }d\]to be the initial term and the normal contrast of the A.P. separately. Then, at that point, it given that
If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
How about we take \[a\text{ }and\text{ }d\]to be the initial term and the normal contrast of the A.P. separately. Then, at that point, it given that Along these lines, the amount of \[\left( p\text{...
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms.
Let \[a1,\text{ }a2,\text{ }and\text{ }d1,\text{ }d2\]be the initial terms and the normal distinction of the first and second math movement individually. Then, at that point, from the inquiry we...
If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference.
We realize that, \[{{S}_{n}}~=\text{ }n/2\text{ }\left[ 2a\text{ }+\text{ }\left( n-1 \right)d \right]\] From the inquiry we have, On looking at the coefficients of\[{{n}^{2}}\] on the two sides, we...
Find the sum to n terms of the A.P., whose kth term is 5k + 1.
Given, the \[{{k}^{th}}~\]term of the A.P. is . \[5k~+\text{ }1.\] \[{{k}^{th}}~term\text{ }=~{{a}_{k}}~=~a~+\text{ }(k~\text{ }1)d\] And, \[\begin{array}{*{35}{l}} a~+\text{ }\left( k~\text{ }1...
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
Given A.P., \[25,\text{ }22,\text{ }19,\text{ }\ldots \] Here, Initial term, \[a\text{ }=\text{ }25\]and Normal distinction, \[d\text{ }=\text{ }22\text{ }\text{ }25\text{ }=\text{ }-\text{ }3\]...
In an A.P., if pth term is 1/q and qth term is 1/p, prove that the sum of first pq terms is ½ (pq + 1) where p ≠ q.
Solution:-
How many terms of the A.P. -6, -11/2, -5, …. are needed to give the sum –25?
How about we consider the amount of n terms of the given A.P. as \[\text{ }25.\] We realized that, \[{{S}_{n}}~=\text{ }n/2\text{ }\left[ 2a\text{ }+\text{ }\left( n-1 \right)d \right]\] where...
In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112.
Given, The initial term \[\left( a \right)\]of an \[A.P\text{ }=\text{ }2\] How about we accept d be the normal contrast of the A.P. In this way, the A.P. will be \[2,\text{ }2\text{ }+\text{...
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
The regular numbers lying somewhere in the range of \[100\text{ }and\text{ }1000,\]which are products of \[5,\text{ }are\text{ }105,\text{ }110,\text{ }\ldots \text{ }995.\] It plainly frames an...
Find the sum of odd integers from 1 to 2001.
The odd numbers from \[1\text{ }to\text{ }2001\]are\[~1,\text{ }3,\text{ }5,\text{ }\ldots \text{ }1999,\text{ }2001.\] It obviously shapes an arrangement in \[A.P.\] Where, the initial term,...