if a², b²,c² 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+a

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}

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

insert three nos. between 1/3 and 432 so that the resulting sequnce is a G.P

ANS DIS PLZZZ

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 )

 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?

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

Evaluate 3. 3^1/2 . 3^1/4 . 3^1/8 . ................... upto infinity.

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

 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) .

SEQUENCE AND SERIES

TOPIC: nth term of an arithmetic progression

EXAMPLE 7:

PLEASE EXPLAIN WHY WE TAKE FOUR TERMS ASa 3d,ad,a+d,a+ 3d. ????

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

if p^th, q^th, r^thand 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, d are in G.P, prove that are in G.P.

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 integers from 1 to 100 that are divisible by 2 or 5?

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

How many different words can be formed of the letters of the word 'MALENKOV' so that:

1) No two vowels are together.

2) The vowels may occupy odd places

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

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

1. If a,b,c are in A.P and X,Y,Z are in G.P then prove( X^b-c)x (Y^c-a) x(Z^a-b)=1
2. In a G.P t_p+q=m and t_p-q=n. Then find t_p.

pls answer-- in an AP if a_p+1 = 2a_q+1 prove that a_3p+1 = 2a_p+q+1..

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

1. 101, 207, 309
2. 101, 201, 301
3. 2, 6, 9
4. NONE OF THE ABOVE

Find the sum tonterms of the sequence, 6, 66, 666, 6666…

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 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

Which term of the series (28−16𝑖)( 27−14𝑖)( 26−12𝑖) +⋯ is (i) purely real (ii) purely imaginary.

If in an A.P., S_n= n²p and S_m=m²p, then S_p=?

what is the proof of formula : s_n=n/2(2a=(n-1)d

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

If GP is 8,-16,32,-64 THAN,

                                                 THE COMMAN RATIO IS -2

RIGHT OR WRONG

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.

if (b-c)^2, (c-a)^2, (a-b)^2 are in AP prove that 1/(b-c) , 1/(c-a) , 1/(a-b) are in AP.

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 a,b,c arein G.P. , then prove that a² + ab + b² / bc + ca + ab = b + a / c + b

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 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 P²Rⁿ = Sⁿ

Q3.A person was drawing a monthly salary of Rs 2500 in 11th year of servce and a salary of Rs 2900 in the 19th year. Given that pension is half the salary at retirement time, find his monthly pension if he had put in 25 years of service before retirement. Assume that annual increment is constant.

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

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

sum the series

3.8+6.11+9.14+...to n terms

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

 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

Find the sum of n terms of the sequence

( x + 1/x )² , ( x² +1 /x²)²  , (x³  + 1/x³ )² ,..........

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

 find the sum of the following series:1²+3²+5²+..........to n terms.

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 ??