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Syllabus

if a

^{2}, b^{2},c^{2 }are in a A.P .then prove that the following are also in A.P (i) 1/b+c ,1/c+a ,1/a+b (ii) a/b+c , b/a+c ,c/b+a19. Consider a three digit number x

_{1}x_{2}x_{3}such that x_{1}.x_{2}.x_{3}$\in $ N. Then the number of positive integral solutions of x_{1}.x_{2}.x_{3 }= 480 is ${\lambda}^{2}$ -100, then the sum of the digits of $\left|\lambda \right|$ is(A) 8 (B) 9 (C) 7 (D) 10

Find the sum to n terms of the series :- 5 + 11 + 19 + 29 + 41 +..........

^{2}c^{3}is ???Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

If a+b+c not equal to zero and b+c/a,c+a/b,a+b/c are in AP.Prove that 1/a,1/b,1/c are also in AP

Show that a^2,b^2,c^2 are in AP if and only iff 1/b+c,1/c+a,1/a+b are in AP

{Experts can you please clarify my doubts}

a thief runs away from a police station with a uniform speed of100 m per min. after a minute a policeman runs behind him to catch. he goes at a speed of 100 m in 1

^{st }min and increases his speed by 10 m each succeeding min. after how many min, the policeman catch the thief?if p arithmetic means are inserted between a and b, prove that d=b-a/p+1

If the pth, qth and rth terms of a GP be a, b, c respectively, prove that

a^(q-r).b^(r-p).c^(p-q)=1;

where ^=raised to the power

The third term of a GP is 4 , find the product of its first five terms .

( answer = 1024 )

Show that thesum of (

m+n)^{th}and (m-n)^{th}term of an A.P is equal to twice them^{th}term.If a2, b2, c2, are in AP, then show that a/b+c, b/c+a, c/a+b are in AP.

If 1/x,1/y,1/z are AP, show that:

(i) yz,zx,xy are in AP

(ii) xy,zx,yz are in AP

(iii) y+z/x,z+x/y,x+y/z are in AP

I got the first one but how to do the other two?

if (m+1)th term of an AP is twice the n+1th term, prove that (3m+1)th term is twice the (m+n+1)th term.

please answer ASAP, exam tmrw.

if sum of 40 A.Ms between two numbers is 120,find the sum 50 AMs between them.

If 7 times the 7th term of an A.P. is equal to 11 times the 11th term,show that 18th term of A.P. is 0.

ind the sum of n terms of :- 1/2*5+1/5*8+1/8*11+........

The sum of 11 terms of an AP whose middle term s 30 is

(1) 320 (2)330 (3)340 (4)350

If the sum of n terms of an A.P. is 2mn + pn

^{2}, where m and p are constants, find the common differenceSum the series: 1+3+7+15+31+............to n terms.

If a, b , c are in G.P, and x, y be the arithmetic means of a, b and b, c respectively, prove that (i) a/x+c/y=2 (ii)1/x + 1/y= 2/b

If first term ,second , and last term of an A.P be a ,b , c, respectively . Then show that the sum is

(b+c-2a) (a+c) / 2(b-a) .

how many terms of the sequence 18,16,14......should be taken so that their sum is zero.

if p

^{th}, q^{th}, r^{th}and s^{th}terms of an A.P. are in G.P.,show that (p-q),(q-r) and (r-s) are also in G.P.(where summation is from n=1 to n=20)

If

a,b,c,dare in G.P, prove that are in G.P.SEQUENCE AND SERIES

TOPIC: nth term of an arithmetic progression

EXAMPLE 7:

PLEASE EXPLAIN WHY WE TAKE FOUR TERMS AS

a3d,ad,a+d,a+ 3d. ????find the sum of integers from 1 to 100 that are divisible by 2 or 5?

If n is an A.P such that a

_{4}/a_{7}= 2/3, find a_{6}/a_{8}...prove that:2^1/4 . 4^1/8 . 8^1/16............upto infinity=2

Find the sum of 30th term of the sequence 7, 7.7, 7.77, 7.777..................

The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.

If a,b,c are in A.P. and a,b,d are in G.P. ,prove that a,a-b,d-c are in G.P.

let x=1+a+a2+.............. y=1+b+b2+.......... thn prove that

1+ab+a2b2+.......=xy/x+y-1

In an A.P.,s

_{3}=6,s_{6}=3,prove that 2(2n+1)S_{n}_{+4}=(n+4)S_{2n+1}.If the p

^{th},q^{th}terms of a G.P. are q,p respectively ,show that (p+q)^{th}term is (q^{p}/p^{q})^{1/p-q}find the number of terms in the A.P. 3,7,11,........407.Also find 20th term from the end

^{b-c})x (Y^{c-a}) x(Z^{a-b})=1_{p+q}=m and t_{p-q}=n. Then find t_{p}.7^2+9^2+11^2+............n terms

Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

Find the sum to

nterms of the sequence, 6, 66, 666, 6666…if AM between two numbers exceeds their GM by 2 and the ratio of two numbers is 4, find the numbersIf 1/a, 1/b, 1/c are in AP, prove that (i) b + c / a, c +a / b, a + b / c are in AP (ii) a(b +c), b (c +a), c ( a + b) are in AP

solve the equation 2+5+8...+x=155

If in an A.P., S

_{n}= n^{2}p and S_{m}=m^{2}p, then S_{p}=?1+(1+2)+(1+2+3)+(1+2+3+4)... find the sum of the series

if a,b,c, and d are in GP, show that

(b-c)^2 + (c-a)^2 + (d-b)^2 = (a-d)^2

a) 1/2 (root 5) b) root 5 c) 1/2 (root 5 - 1) d) 1/2 (1- root 5 )

100

Sigma 3

^{r}(2-2r)/(r+1)(r+2)r=2

Options : -

(A) 1/2 - {3

^{100}/100(101)}(B) 3/2 - {3

^{101}/101(102)}FIND FOUR NUMBERS IN AP WHOSE SUM IS 20 &SUM OF WHOSE SQUARES IS 120

The difference between any two consecutive interior angles of a polygon is 5°.If the smallest angle is 120°, find the number of the sides of the polygon.

In the arithmetic progression 2,5,8....upto 50 terms,and 3,5,7,9....upto 60 terms ,find how many pairs are identical and find the identical pairs.

three numbers are in A.P. and their sum is 15 , if 1, 4 and 19 are added to these numbers respectively the resulting numbers are in G.P.. find the numbers.

the sum of 4 numbers in a.p is 40 and the product of their extremes is 91.the number are

The sum of an infinite number of terms of GP is 4 and the sum of their cubes is 192. Find the series.

The sum of first two terms of an infinite G.P. is 5 and each terms is three times the sum of the succeeding terms. Find the G.P.

if x1,x2,x3 ....xn are in H.P then prove that x1x2+x2x3+x3x4+....+xn-1xn =( n-1)x1xn

_{k}a_{k-1 }+ a_{k-1}a_{k-2} = 2a_{k}a_{k-2 }, k>=3 and a_{1}=1 , here S_{p}= sigma (k = 1 to k = p) 1/a_{k }and given that S_{2p}/S_{p }does not depend on p then 1/a_{2016 }is = ?the sum of three numbers in GP is 56. if we subtract 1, 7, 21 from these numbers in that order, we obtain an AP. find the numbers.

If one A.M.,

Aand two geometric meansG_{1}_{ }andG_{2}_{ }inserted between any two positive numbers,show thatG._{1}^{2}/ G_{2}+ G_{22}/ G_{1 }= 2A1.If the AM ,GM and HM of the first and last terms of the series 25,26,27,.....N-1,N are the terms of the series,find the value of N?

2.The sum of all possible products of the first 'N' natural numbers taken two bu two is:

a)1/24n(n+1)(n-1)(3n+2)

b)n(n+1)(n-1)(2n+3)/24

c)n(n+1)(n-1)(2n+1)/6

d) none of these

if in a gp the (p+q)th term is a and (p-q)th term is b , prove that the pth term is sqrt (ab).

pth term of an A.P. is 'a' and qth term is 'b'. prove that sum of (p+q)th term is p+q/2[a+b+(a-b/p-q)]. plz ans needed soon.....

_{c}a, log_{b}c, log_{a}b are in A.P. then find the common difference of the A.P.Let S be the sum, P be the product and R be the sum of reciprocals of n terms in a G.P. Prove that P

^{2}R^{n}= S^{n}2. SUM 1 + 3/4+7/16+15/64+31/256+.....TO INFINITY

SUM 1+2/2+3/2^2+4/2^3+.......TO N TERMS

sum of an infinite gp is 57 and sum of their cube is 9747 find the gp

Must reply me the solution please!URGENT IMPORTANT:___________

1) The 2nd, 31st and the last terms of an AP are 31/4 , 1/2 , -13/2 respectively. Find the first term and the number of terms.

_ _ _

2) How many two-digits numbers are divisible by 7?

let x=1+a+a^2........ and y=1+b+b^2..... , where modulus(a)

1+ab+a^2b^2.......=xy/(x+y-1)

please i have a test tommorow.....!!

^{2}, q^{2}, b^{2}are in A.PProve that a,b,c are in A.P. iff 1/bc,1/ca,1/ab are also in A.P.

the sum of first n terms of the series 1square + 2* 2square + 3square +2*4square + 5square + 2*6square +... is n*(n+1)square/2 when n is even. What is the sum when is odd?

The number 1111.....1(91 times) is a

A) prime b) non prime c) even

If p , q, r are in G.P and the equation px^2 + 2qx + r = 0 and dx^2 + 2ex + f = 0 have a common root , then show that d/p , e/q , f/r are in A.P.

Find two numbers whose difference is 2 and whose AM exceeds the GM by 1/2.The sum of the infinite G.P is 15, Sum of squares of 3 terms of the g.p is 45. Find the series.

Find the sum of sequence, 7, 77, 777, 7777..... to n terms ???

plz ans fast....

its very urgent

$2.Ifxyz=\left(1-x\right)\left(1-y\right)\left(1-z\right)where0\le x,y,z\le 1,thentheminimumvalueofx\left(1-z\right)+y\left(1-x\right)+z\left(1-y\right)is:\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(a\right)\frac{3}{2}\left(b\right)\frac{1}{4}\left(c\right)\frac{3}{4}\left(d\right)\frac{1}{2}$

5+55+555...n terms. Change this term into G.P. then find the sum of this series?

Insert 8 arithmetic means between 17 and 53.

If (a1,a2,a3......an) are in A>P> with common difference d. then the sum of the series: sin d [cosec a1.cosec a2 + cosec a2.cosec a3 +........+ cosec a(n-1).cosec an ] is what ??

if the nth term of a GP is 128 and the sum of its n terms is 225.if the common ratio is 2, then the first term of the GP is????