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+a

find the sum of the sequence 2,22,222,.......to n terms

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

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 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?

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 squares of the first n natural numbers is given by to prove it why we are taking cubes its squares right

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.

For what values of k,the numbers ... 1+k,5/6 + k,13/18 + k are in G.P.

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

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

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

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 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) .

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

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

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

^{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 the sequence 2,22,222,.......to n terms

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

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

the first term of the GP is 85, the sum of second term of AP and the second term of the GP is

76 and that of the 3rd term of AP and 3rd term of GP is 84. The sum of the AP is 126. Find each

term of AP and GP

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

^{1/n}-n (B)greater than or equal to n(n+1)^{1/n}/(n+5) (C)less than n(n+1)^{1/n}- n (D) equal to n(n+1)^{1/n}- nThe third term of a GP is 4 , find the product of its first five terms .

( answer = 1024 )

The sum of squares of the first n natural numbers is given by to prove it why we are taking cubes its squares right

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.

For what values of k,the numbers ... 1+k,5/6 + k,13/18 + k are in G.P.

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

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

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

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

^{x}=b^{y}=c^{z},where x,y,z are unequal positive number and a,b,c are in G.P.,then x^{3}+z^{3}is? (Answer is >2y^{3}but how?)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 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) .

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

Evaluate 3. 3

^{1/2}. 3^{1/4}. 3^{1/8}. ................... upto infinity.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.