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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+aFind the sum of n terms of the sequence

( x + 1/x )

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

the sum of all possible products of first n natural numbers taken two at a time is

ANS:(1/24)*n(n+1)(n-1)(3n+2)

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 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

let a

_{1}, a_{2}, ..... a_{11}be real numbers satisfying a_{1}= 15 27 -- 2a_{2}0 a_{k}= 2a_{k-1}-- a_{k --2 }for k = 3,4, ........11. if (a_{12}+ a_{22}+ ....a_{112}) /11 =9 then find the value of (a_{1}+a_{2}+ ......... a_{11}) / 11The third term of a GP is 4 , find the product of its first five terms .

( answer = 1024 )

If a is the A.M between b and c and g1, g2 are two geometric means between b and c. show that g13+g23=2abc.

If a2, b2, c2, are in AP, then show that a/b+c, b/c+a, c/a+b are in AP.

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.

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

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

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

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}

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) .

In an increasing G.P the sum of the first and last term is 66,the product of the second and the last but one is 128 and the sum of the terms is 126.How many terms are there in the progression?

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

Which term of the sequence 8-6i,7-4i,6-2i,...... is (i) purely real (ii) purely imaginary?

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.If 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

find the sum of integers from 1 to 100 that are divisible by 2 or 5?

The sum of series 1/2! + 1/4! + 1/6! + ..... isprove that:2^1/4 . 4^1/8 . 8^1/16............upto infinity=2

Find the sum the following series to n terms:

3+7+14+24+37+.........

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

If S denotes the sum of an infinite G.P. , S

_{1 }denotes the sum of the squares of its terms,then prove that the first term and common ratio are respectively 2SS_{1}/ S^{2}+ S_{1 }and S^{2 }- S_{1}/ S^{2 }+ S_{1}.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 x1,x2,x3 ....xn are in H.P then prove that x1x2+x2x3+x3x4+....+xn-1xn =( n-1)x1xn

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

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

^{2}, where m and p are constants, find the common differenceFind the sum to

nterms of the sequence, 6, 66, 666, 6666…If in an A.P., S

_{n}= n^{2}p and S_{m}=m^{2}p, then S_{p}=?If a, b, c are in AP, prove that 1/(√b+√c), 1/(√c+√a), 1/(√a+√b) are in AP.

1+(1+2)+(1+2+3)+(1+2+3+4)... find the sum of the series

If (b+c-a)/a , (c+a-b)/b & (a+b-c)/c are in A.P., then prove that 1/a, 1/b & 1/c are also in A.P. ...... answer urgently needed!!

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

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.

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.

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.

B={x:x is multiple of 5} then A-B is?

a) A intersection B

b)A intersection B dash

c) A dash intersection B dash

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.

_{c}a, log_{b}c, log_{a}b are in A.P. then find the common difference of the A.P.The sum of an infinite number of terms of GP is 4 and the sum of their cubes is 192. Find the series.

$89.\mathrm{If}{\mathrm{a}}_{1},{\mathrm{a}}_{2},{\mathrm{a}}_{3},{\mathrm{a}}_{4}\mathrm{are}\mathrm{in}\mathrm{H}.\mathrm{P}.,\mathrm{then}\frac{1}{{\mathrm{a}}_{1}{\mathrm{a}}_{4}}\sum _{\mathrm{r}=1}^{3}{\mathrm{a}}_{\mathrm{r}}{\mathrm{a}}_{\mathrm{r}+1}\mathrm{is}\mathrm{a}\mathrm{root}\mathrm{of}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{A}\right){\mathrm{x}}^{2}+2\mathrm{x}+15=0\left(\mathrm{B}\right){\mathrm{x}}^{2}+2\mathrm{x}-15=0\phantom{\rule{0ex}{0ex}}\left(\mathrm{C}\right){\mathrm{x}}^{2}-6\mathrm{x}-8=0\left(\mathrm{D}\right){\mathrm{x}}^{2}-9\mathrm{x}+20=0\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

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.

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

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.

find the general term of progression 1/4,-1/2,1,-2....

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 a , b , c are in AP then prove that (a-c)

^{2}= 4(b^{2 }- ac).if x, y, z are in GP and log

^{a}_{ b }. x log^{c}_{b }= 1 , then show that a^{x}= b^{y}= c^{z}.plz any1 answer quickly.. its urgent....

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.....

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}If x,y,z are in A.P., show that (x+2y-z)(2y+z-x)(z+x-y)=4xyz

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

the sum of n terms oof two ap are in the ratio(7n-5) :(5n+17).Show

that their 6th term are equal.

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

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.....!!

Find the sum of the series 2+11+101+1001+… to n terms.

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

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.

^{3}- 24x^{2}+ 23x + 18 = 0, then find S_{19}.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 THE SERIES 2+6+ +18 +.......... + 4374 .

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

The value of 0.2

^{log (root 5) [1/4+1/8+1/16+......]}is(1) 4 (2) log 4 (3) log 2 (4) none

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

plz ans fast....

its very urgent

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