The ratio of the sum of n terms of two A.P.s is (7n+1):(4n+27).Find the ratio of their mth term.

if 3x+k,2x+9 and x+13 are three consecutive terms of an AP.,Find k.

1. The ratio of the sums of m and n terms of an AP is m² : n^2. show that the ratio of the m^th and n^th terms is (2m-1) : (2n-1)
2. In an AP, the sum of first n terms is 3n²/2 + 5n/2, find its 25^th term.

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last terms to the product of the two middle terms is 7 : 15. Find the numbers.

if 1+2+3+..............+n = 666, find the value of n.

If the m^th term of an A.P. be 1/n and n^th term be 1/m, then show that its (mn)^th term is 1.

IF THE SUM OF FIRST m TERMS OF AN AP IS n. AND THE SUM OF FIRST n TERMS IS m, THEN SHOW THAT THE SUM OF ITS FIRST( m+n) TERMS IS -(m+n).

Maths Project :make designs using arithmetic  progression
 

if the pth term of an A.P is q and the qth term is p, prove that its nth term is (p+q-n)

If the nth term of a G.P. be p, then show that the product of the first (2n-1) terms is p^2n-1.

the sum of the first n terms of an AP is given by s_n=3n²-n , determine the AP and its 25^thterm.

If m times the mth term of an A.P is equal to n times its nth term, show that the (m+n)th term of the A.P is zero.

the sum of first six terms of an ap is 42 .the ratio of its 10th term is and its 30th term is 1:3. calculate the first and thirteenth term

 8. In 4ABC, A = 25

The sum of the third and seventh term of an A.P. is 6 and their product is 8. Find the sum of the first sixteen terms of the A.P. .

If pth , qth and rth term of an AP are a,b,c respectively , then show that

(a-b)r +(b-c)p + (c-a)q = 0

Please help me with this question asap .

Find four numbers in A.P such that their sum is 16 and their product is 105.

 150 workers were engaged to finish a piece of work in a certain no. of days. 4 workers droped d 2nd day, 4 more workers droped the 3rd day n so on..... it takes 8 more days to finish the work now ..find d no. of days in vch the work waz completed....

Find the sum of 20 terms of the series

1² - 2² + 3² - 4² + 5² - 6² + ........ 20 terms.

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the

1. Every square in the grid will contain one number.

3. You will not repeat the same number in a row or column.
4. The areas that are outlined with a thick dark line are called cages. Each cage will contain one square with a number on the top left, which is called the target number. The numbers in the squares within a cage must create the target number using addition, subtraction, multiplication, or division. The symbol next to the target number tells you what operation to use.
   For subtraction and division, the numbers can be in any order as long as the smaller number subtracted from (or divided into) the larger number equals the target. 
5. Cages with just one square should be filled in with the target number in the top corner. These are called freebies. Freebies will not have a symbol next to the target number. Many KenKen puzzle solvers like to start with the freebies, if there are any.

A KenKen puzzle with a few labels is shown below. For emphasis, a variety of colors were used to denote the different cages outlined by the thick dark lines.

If the sum of first 7 terms of an AP is 49 and that of first 17 terms is 289.Find the sum of first n terms

The sum of n terms of two ap are in ratio (5n+4) : (9n+6) Find the ratio of their 18th term?

plzz reply with solution

 how to multiply 15=a+2d by 25= 2a+9d please anwer just now as my test is tomoorow

the ratio of the sum of n terms of two AP's is (7n+1):(4n+27).find the ratio of their m th terms.

Answer: let a1 , a2 be the 1st terms and d1 , d2 the common differences of the two given A.P's. then the sums of their n terms are given by

Sn = n/2 {2.a1+(n-1)d1} and Sn' = n/2{2. a2 +(n-1)d2}

Sn/Sn' = n/2{2.a1+(n-1)d1} / n/2{2.a2 + (n-1)d2}

Sn / Sn' = 2.a1+(n-1)d1 / 2.a2 + (n-1)d2

it is given that

Sn / Sn' = 7n+1 / 4n + 27

2.a1 + (n-1)d1 / 2.a2 + (n-1)d2 = 7n+1 / 4n+27 ........................ (i)

To find the ratio of the mth terms of the two given AP's , we replace n by (2m-1) in equation (i)

therefore, 2.a1 + (n-1)d1 / 2.a2 + (n-1)d2 = 7(2m-1) + 1 / 4(2m-1) + 27

a1 + (m-1)d1 / a2 + (m-1)d2 = 14m - 6 / 8m + 23

Hence, the ratio of the mth terms of the two A.P's is (14m - 6) : (8m + 23)

My question is, why it has been assumed (2m-1) in the place of 'n' ? has it been arrived from solving with the help of a formula or is it a mere assumption? if it is simply an assumption, why it should be assumed as (2m-1) ? why not 2m or (m - 1)

A lamp lighter has to light 100 gas lamps. He takes one and half minutes to go from one lamp post to the next. Each lamp burns 10 cubic feet of gas per hour. How many cubic feet of gas has been burnt by 8.30pm, if he lights the first/last lamp at 6pm

If s_n, the sum of first n terms of an AP is given by s_n= (3n²-4n), then find its nth term.

If the sum of m terms of an A.P is the same as the sum of n terms of the same A.P, show that the sum of its (m+n) terms is zero.

what are the uses of arithmetic progressions in daily life? i want atmost 10, pls help me as soon as possible

A student taking test consisting of 10 quetions is told that each after the first is worth 2 mks more than the preceding ques. If 3rd ques. of the test is worh 5 mks..,what is the maximum score that the student can obtain by attempting 8 questions.

if the nth term of an AP is (2n+1) find the sum of first n terms of the AP

If S_n =(3n²+2n) , find the first term and the common difference of the AP.

sum of first p , q and r terms of an A.P. are a , b and c respectively. Prove that :

a/p (q-r) + b/p(r-p) + c/r (p-q) = 0

If S₁ , S₂ , S₃ are the sum of n terms of three AP's the first term of each being unity and respective common diffrence being 1 , 2 , 3_ _ _ _ _. Prove that S₁+S₃= 2S2.

which term of an AP 3,15,27,39............ will 132 more than its 54^th term

The sum of n terms of two AP are in the ratio (2n+3):(6n+5),then the ratio of their 13th terms is 
(a) 53:155
(b)29:83
(c) 31:89
(d)27:8
Please answer with complete steps and explanation. 

Divide 56 into 4 parts which are in AP such that hte ratio of product of extremes to the product of mean is 5 : 6? Hoping for a quick response......plz.....[ May be within Sunday ]

if sum of n terms of an AP 2n² + 5n, then find its n^th term.

 find the sum of all the natural numbers between 200 and 300 which are divisible by 4.

help plsss

In an AP,the sum of first n term is 3n2/2+13n/2

find its 25th term

 solve the solution 1+4+7+10.............+x = 287

if Sn denotes the sum of first n terms of an A.P., prove that S12=3(S8-S4).

how many multiples of 4 lie between 100 and 250.also find its sum

the sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. find the first 3 terms of the AP.

Divide 32 into 4 parts which are in A.P. such that the product of extremes is to the product of means is 7:15.

the 10th & 20th termof an AP are 73 & 143 find the 1st term the common difference & 30th term of AP

30) the digits of a positive integer,having three digits are in A.P. and their sum is 15.the number obtained by reversing the digits is 594 less than the original number.find the number.

Find the LCM of (x + 3)(6x² + 5x+ 4) and (2x² + 7x + 3) (x + 3)

Hint:

Find the sum of all the integers between 100 and 200 that are not divisible by 9

In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.

the 12th term from the end in the AP 9,5,1.....is -107.Find the last term

 The sum of n 2n 3n terms of an AP are S1 S2 S3 respectively. Prove that S3=3(S2-S1).

Find the sum of first five multiples of 3?

Which term of AP:121,117,113,......., is its first negative term?

 Which term of the sequence 7.3, 6.9, 6.5, 6.1, .... is the first negative term?

The angles of a quadrilateral are in a.p. whose common difference is 10degree.Find the angles.

 If there are (2n+1) terms in A.P,then prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n.

 Find the 20th term from the last term of the AP 3, 8, 13, .....253.

If s_n denotes the sum of n terms of AP whose common difference is d and first term is a, find s_n-2s_n-1+s_n-2

Show that sum of an AP whose first term is a,the second term b and the last term c,is equal to (a+c)(b+c-2a)/2(b-a)..Plzzz i need hlpp!!!!

if the Pth term of an AP is Q and its Qth term is P then show that its (P+Q)th term is zero/

The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.

in an AP,the sum of first ten terms is -150 and the sum of its next ten terms is -550.Find the AP.

if sn denotes the sum of first n trems of an ap, prove that s12=3(s8-s4)

THE ANGLES OF A TRIANGLE ARE IN A.P.THE GREATEST ANGLE IS TWICE THE LEAST.FIND ALL THE ANGLES OF THE TRIANGLE.