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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.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.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)

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. .

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

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....

Answer given:1050+1260-300=2010

Please explain with working.

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.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 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

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

Q) 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?

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

the number of odd numbers between 60 and 360 is

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

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

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.

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

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.

CASE STUDYBal Bharti Vidyalaya is located in Karauli district of Rajasthan. The school decided to go for

plantation drive on the occasion of VANMAHOTSAVA. It was decided that the number of

trees, that each section of each class will plant, will be the same as the class in which they

are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees

and so on, till Class X. There are five sections of each class. Ms. Anshu Sharma, Principal of

the Vidyalaya asked forest department to provide plants for Vanmahotsava.

(A) How many plants were needed for plantation by all sections of class IV?

(i) 20

(ii) 25

(iii) 30

(iv) 35

(B) How many plants were needed for plantation by all sections of Primary classes (1st to 5th)?

(i) 65

(ii) 75

(iii) 25

(iv) 35

(C) How many plants were needed for plantation by all sections of class 7?

(i) 30

(ii) 35

(iii) 40

(iv) 45

(D) How many plants were needed for plantation by the whole school?

(i) 300

(ii) 275

(iii) 250

(iv) 200

(E) How many plants were needed for plantation by classes 6th to 8th?

(i) 105

(ii) 100

(iii) 80

(iv) 120

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.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)

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.Ram asks the labour to dig a well upto a depth of 10 metre . Labour Charges Rs 150 for first metre and Rs .50 for each subsequent metres . As the labour was uneducated , he claims Rs.550 for the whole work . What shoulld be the actual amount to be paid to the labours . ?

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

1 2 9

3 4 _

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

Find the sum of first five multiples of 3?

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

a)Find the expression for number of plants in the nth row.

i) 2n + 1

ii) 2n − 1

iii) 4n − 1

iv) 2n + 3

b) Find the number of plants in the 7th row.

i) 21

ii) 7

iii) 15

iv) 17

c) If there are 25 plants in the last row, find the total number of rows.

i) 11

ii) 10

iii) 13

iv) 12

d) Assuming that Reema has kept distance between any two consecutive plants

in a row as 30 cm, find the length of the 12th row (i.e. the distance between

the first and the last plant in the 12th row neglecting the width of the plants).

i) 7.5 metres

ii) 7.2 metres

iii) 6.9 metres

iv) 7.0 metres

e) Reema’s father gifts her 50 more plants. She continues to arrange these

plants in Arithmetic Progression. She observes that she is falling short of

some plants to complete the A.P. How many minimum number of plants

does she require more to complete the A.P. ? (Assuming 25 plants in the last

row before her father gifts her 50 plants).

i) 6

ii) 7

iii) 8

iv) 5

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.

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,...

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!!!!

Find the sum of 10 terms of the sequence 5, 5.5, 5.55, 5.555,.....

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/

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

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)

there are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres.a gardener waters all the trees separately starting from the well and he returns to well sfter watering each tree to get water for the next.find the tatal distance the gardener will cover in order to water all the trees.

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