Call me

Have a Query? We will call you right away.

+91

E.g: 9876543210, 01112345678

We will give you a call shortly, Thank You

Office hours: 9:00 am to 9:00 pm IST (7 days a week)

What are you looking for?

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+aIf 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}

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

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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?What is the next number of the given series:-

4,10,34,94,214,424...

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 )

If a

^{2}+2bc,b^{2}+2ac,c^{2}+2ab are in A.P. ,show that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.If a2, b2, c2, are in AP, then show that a/b+c, b/c+a, c/a+b are in AP.

7^2+9^2+11^2+............n terms

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 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.

pls answer-- in an AP if a

_{p+1}= 2a_{q+1 }prove that a_{3p+1}= 2a_{p+q+1..}The sum of 11 terms of an AP whose middle term s 30 is

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

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.

Sum 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

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

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) .

if tan(alpha+theta) = ntan (alpha-theta) then show that : (n+1)sin 2theta=(n-1)sin 2alpha

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

2.1+3.2+4.4+5.8+.....

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.If

a,b,c,dare in G.P, prove that are in G.P.find the sum of integers from 1 to 100 that are divisible by 2 or 5?

Q4 A person purchases a television set for Rs 16000. Its life is estimated to be 20 years. If the yearly depreciation is assumed to be constant, find the rate of depreciation and the price after 8 years.

prove that:2^1/4 . 4^1/8 . 8^1/16............upto infinity=2

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

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

1+ab+a2b2+.......=xy/x+y-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}^{b-c})x (Y^{c-a}) x(Z^{a-b})=1_{p+q}=m and t_{p-q}=n. Then find t_{p}.if the sum of first four terms of an AP IS P AND THE SUM OF FIRST 8 TERMS IF IS Q AND SUM OFfirst 12 terms is r. express 3p+r in terms of q

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

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?

Find the sum to

nterms of the sequence, 6, 66, 666, 6666…^{x}-1-x)/x^{2}in ascending powers of x ,the 4^{th} term isIf 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

If in an A.P., S

_{n}= n^{2}p and S_{m}=m^{2}p, then S_{p}=?In an A.P.,s

_{3}=6,s_{6}=3,prove that 2(2n+1)S_{n}_{+4}=(n+4)S_{2n+1}.1+(1+2)+(1+2+3)+(1+2+3+4)... find the sum of the series

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

If the 5th term of an A.P. is 1/10 and the 10th term is 1/5 then find the 50th term of an A.P.

FIND FOUR NUMBERS IN AP WHOSE SUM IS 20 &SUM OF WHOSE SQUARES IS 120

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?

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.

If a,b,c arein G.P. , then prove that a

^{2 }+ ab + b^{2}/ bc + ca + ab = b + a / c + bthree 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 an infinite number of terms of GP is 4 and the sum of their cubes is 192. Find the series.

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 ??

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 AM between two numbers exceeds their GM by 2 and the ratio of two numbers is 4, find the numbersif x1,x2,x3 ....xn are in H.P then prove that x1x2+x2x3+x3x4+....+xn-1xn =( n-1)x1xn

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 }= 2Aif 1/a,1/b,1/c are in a.p .prove that a/c=(a-b)/(b-c).

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).

WHAT IS THE REMAINDER WHEN 30

AND WHAT IS THE REMAINDER WHEN 43^{40}IS DIVIDED BY 17^{86}IS DIVIDED BY 5? IS THERE ANY TRICK TO SOLVE SUCH QUESTIONS? PLEASE,PLEEEEEEEEASE MA'AM/SIR HELP ME OUT OF THIS PROBLEMpth 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.....

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

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

if p arithmetic means are inserted between a and b, prove that d=b-a/p+1

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.....!!

Prove that a,b,c are in A.P. iff 1/bc,1/ca,1/ab are also in A.P.

1.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

Find the sum of n terms of the sequence

( x + 1/x )

^{2}, ( x^{2}+1 /x^{2})^{2}, (x^{3}+ 1/x^{3})^{2},..........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.

The sum of the infinite G.P is 15, Sum of squares of 3 terms of the g.p is 45. Find the series.

If p,q,r are in A.P. and x,y,z are in G.P. ,prove that x

^{q-r}y^{r-p}z^{p-q}=1.Find the sum of sequence, 7, 77, 777, 7777..... to n terms ???

plz ans fast....

its very urgent

If a constant is multiplied to each term of an A.P., the resulting sequence will also be an A.P.

If a constant is divided from each term of an A.P., the resulting sequence will also be an A.P.

This is written in the study material but in these two cases the common difference is not constant then how these are A.P. PLZ. ANS. FAST...5+55+555...n terms. Change this term into G.P. then find the sum of this series?

S1,S2,S3,...Sn are sums of n infinite geometric progressions. The first terms of these progressions are 1,2

^{2}-1,2^{3}-1,...2^{n}-1 and the common ratios are 1/2,1/2^{2},1/2^{3}...1/2^{n}. Calculate the value of S1+S2+...+Sn