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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+aThe number 1111.....1(91 times) is a

A) prime b) non prime c) even

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

in G.P the first term and common ratio are both 1/2(root3+i), then the absolute value of its nth term is:

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

(where summation is from n=1 to n=20)

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?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)

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

What is non constant A.P.

?

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

( answer = 1024 )

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

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

3+5+9+17+33+.....to 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.

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

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

Sum the series: 1+3+7+15+31+............to n terms.

_{c}a, log_{b}c, log_{a}b are in A.P. then find the common difference of the A.P.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) .

Find the sum of n terms of the series the rth term of which is (2r+1)2^r

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.The largest term common to the sequence 1,11,21,31,.... to 100 terms and 31,36,41,46,..... to 100 terms is (A) 381 (B) 471 (C) 281 (D) none . Please give the solution alse.

If

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

If S

_{1},S_{2},S_{3}denote the sum of first n_{1},n_{2},n_{3}terms respectively of an A.P.,then {S_{1}(n_{2}-n_{3})}/n_{1}+ {S_{2}(n_{3}-n_{1})}/n_{2}+{S_{3}(n_{1}-n_{2})}/n_{3}=(A) 0 (B) 1 (C) S

_{1}S_{2}S_{3}(D) n_{1}n_{2}n_{3 Give the process also .}if the first and (2n-1)th terms of an AP,GP HP are equal and their nth term are a,bc respectively, then

1 a=b=c 2a+c = b 3 abc and ac-b

^{2}=0 4none of theseThe 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}.Find the sum of the series : 1 + (1/3) + (1.3/3.6) + (1.3.5/3.6.9) + ........... infinity. ( notation dot (.) here implies multiplication)

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

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

Find the sum to

nterms of the sequence, 6, 66, 666, 6666…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

The sum of series 1/2! + 1/4! + 1/6! + ..... isIf 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

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

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

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)}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.

If S

_{r}denotes the sum of r terms of an A.P. and S_{a}/a^{2}= S_{b}/b^{2}= c . Then S_{c}is(A) c

^{3}(B) c/ab (C) abc (D) a+b+c . Give the process also .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.

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.

Then prove that a (1/b + 1/c ) , b (1/c + 1/a ), c (1/a + 1/b ) are in AP

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.

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?

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 }= 2AThe sum of n terms of two A.P's are in the ratio of (7n-5)/(5n+17). Then the ________ terms of the two series are equal.

A) 12 B) 6 C) 3 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.....

Que. Evaluate : 1+ 2.2+ 3.2^2+ 4.2^3+.......+ 100.2^99

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..................

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.....!!

The first term of an AP is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.

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

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.

if pth term of a gp is p and qth term is q.prove that the nth term is (p (to the power n-q) /q (to the power n-p) ) to the power 1/p-q

an insect start from a point and travel in a straight line 1.5 mm in first second and one third of the distance covered in the previous second in the succeeding second .in how much time would it reach a point 2.5 mm away from its starting point?

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

If a1,a2,a3,------an are in AP then prove that a1

PLEASE I WANT ANSWER FOR THIS AS SOON AS POSSIBLE.^{2}-a2^{2}+a3^{2}-a4^{2}+-------+a_{2n-1}^{2}-a_{2n}2=n/2n-1(a1^{2}-a_{2n}^{2})5+55+555...n terms. Change this term into G.P. then find the sum of this series?

^{2}^{}+....... (till infinity) (mod of x < 1)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 ??