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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
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.
What is the next number of the given series:-
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 1st min and increases his speed by 10 m each succeeding min. after how many min, the policeman catch the thief?
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.
If the pth, qth and rth terms of a GP be a, b, c respectively, prove that
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 4 numbers in a.p is 40 and the product of their extremes is 91.the number are
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.
THE THIRD TERM OF A G.P IS 2/3 & THE 6TH TRERM IS 2/81 FIND THE 8TH TERM
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
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.
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 sum of 40 A.Ms between two numbers is 120,find the sum 50 AMs between them.
how many terms of the sequence 18,16,14......should be taken so that their sum is zero.
if pth, qth, rthand sth 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.
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.
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
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
If the pth,qth terms of a G.P. are q,p respectively ,show that (p+q)th term is (qp/pq)1/p-q
Find the sum of all
natural numbers lying between 100 and 1000, which are multiples of 5.
Find the sum tonterms 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
If in an A.P., Sn= n2p and Sm=m2p, then Sp=?
1+(1+2)+(1+2+3)+(1+2+3+4)... find the sum of the series
if a,b,c are in a G.P ,prove that log a,log b,log c are in an A.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.
If Sr denotes the sum of r terms of an A.P. and Sa/a2 = Sb/b2 = c . Then Sc is
(A) c3 (B) c/ab (C) abc (D) a+b+c . Give the process also .
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 one A.M., A and two geometric means G1 and G2 inserted between any two positive numbers,show that G12/ G2 + G22/ G1 = 2A.
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 all possible products of first n natural numbers taken two at a time is
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
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.
the sum of the series 24,3,8,1,3,7...to 8 term is
b) 36 [13/30]
c) 36 1/9
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).
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?
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
Find the sum of 30th term of the sequence 7, 7.7, 7.77, 7.777..................
is 0,0,0,...0 an arithmetic progression
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)
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.
the sum of first 15 terms of A.P. is 105 and the sum of next 15 terms is 780. find the 3rd term.
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:
d) none of these
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.
Find the sum of sequence, 7, 77, 777, 7777..... to n terms ???
plz ans fast....
its very urgent
What is the sum of the series to 7 terms?
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 ??
If the sum of n terms of an AP is given by Sn =(3n2+4n),find the rth term.
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