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Syllabus

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.

^{2 }: n^{2.}show that the ratio of the m^{th}and n^{th}terms is (2m-1) : (2n-1)^{2}/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.Show that P-7, P-10, P-13, P-16, P- 19,....... are in A.P. find its 8th term and it's common difference.

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).

For the A.P -3, -7, -11,..... can we directly find a

_{30}- a_{20}without actually finding a_{30}and a_{20}? Give reasons for your answer.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)

Q.1. What is the missing number in the pie below?

the sum of the first n terms of an AP is given by s

_{n}=3n^{2}-n , determine the AP and its 25^{th}term.shalini purchased national saving certificate of Rs. 5000 on her daughter's birthday and decided the of Rs 500 on every subsequent birhtday. how much money she will be able to save by her 18th birthday ?

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.

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

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

the nth term of an AP is given by a

_{n}= 4n - 5,then find the sum of first 25 terms of the AP.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. .

Answer given:1050+1260-300=2010

Please explain with working.

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 .

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....

the sum of three numbers in A.P. is 33 and the sum of their cubes is 5409. find the numbers?

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

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

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

If s

_{n}, the sum of first n terms of an AP is given by s_{n}= (3n^{2}-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

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

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

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 Sn denotes the sum of n terms of an AP and if S1= 6 , S7 = 105 , then show that Sn : S(n-3) = (n+3) : (n-3)

If S

_{1}, S_{2}, S_{3}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 S_{1}+S_{3}= 2S2.which term of an AP 3,15,27,39............ will 132 more than its 54

^{th}termQ) The sum of the first five terms of an AP is 25 and the sum of its next five terms is -75.Find the 10th term of the AP?

Q)In an AP the first term is 8 and the common difference is 7.If the last term of the AP is 218,find its middle term?

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 ]

the sum of the two numbers is 25 and the reciprocals is 3/10. find the numbers

if sum of n terms of an AP 2n

^{2}+ 5n, then find its n^{th}term.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

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

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

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.

1 2 9

3 4 _

5 6 341 plz answer fast options 91, 35,19,121,144

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.

Q.Find the common difference of an A.P in which ${a}_{16}-{a}_{12}=16$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.

the number of odd numbers between 60 and 360 is

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.A

contractoremployed150 labourersto finish a peice of work in a certain no. of days.4 workerswent away thesecond day,4 more workerswent away thethird dayandso on. Ifit took 8 more daysto finish the work ,find the no. of days in which the work was completed.

ANURAG.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 the ap 3,10,17 will be 84 more than its 13th term?

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

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

help plsss

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/

write the ap whose second term is 13 and the difference of the 4th term from the 8th term is 16.

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.

There are 25 trees at equal distance of 5 meters in a line with a well ,the distance of the well from the nearest tree being 10 meters .A gardner waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next .Find the total distance the gardner will cover in order to water all the trees .

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

find the first negative term of the AP 2000,1990,1980,1970.....

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

31. For what value of m are the m

^{th}terms of the following two A.P.s the same?(i) 1, 3, 5, 7,....

(ii) 4, 8, 12, 16,...