Sequence and Series questions
1035 published questions with worked solutions.
- If a,b,c are in H.P., then a b+c , b c+a , c a+b will be in
- If the sum of an infinitely decreasing G.P. is 3, and the sum of the squares of its terms is 92, the sum of the cubes of the...
- If H_1,H_2, ,H_n be n harmonic means between a and b, then H_1+a H_1-a + H_n+b H_n-b is equal to
- The sum of the squares of three distinct real numbers which are in G.P. is S^2. If their sum is S, then
- For a sequence a_n , a_1=2 and a_ n+1 a_n = 13. Then _ r=1 ^ 20 a_r is
- If 1a+ 1c+ 1 a-b + 1 c-b =0 and b a+c, then a,b,c are in
- If a,b,c are in G.P. and a-b, c-a and b-c are in H.P., then a+4b+c is equal to
- If a,b,c are in G.P., then _ax, _bx, _cx are in
- If three numbers are in G.P., then the numbers obtained by adding the middle number to each of these numbers are in
- If 3+5+7+ +n terms 5+8+11+ +10 terms =7, then the value of n is
- If a,b,c are in H.P., then 1 b-a + 1 b-c =
- If the m^ th , n^ th and p^ th terms of an A.P. and G.P. be equal and be respectively x,y,z, then
- If 1^2+2^2+3^2+ +2003^2=(2003)(4007)(334) and 1 2003+2 2002+3 2001+ +2003 1=(2003)(334)x, then x=
- If 2, (2^x-1 ) and (2^x+3 ) are in A.P., then 2,2^x-1,2^x+3 are in
- If in an A.P. a_1= _ 10 a, a_ n+1 = _ 10 b and a_ 2n+1 = _ 10 c, then a,b,c are in
- If p^ th ,q^ th ,r^ th and s^ th terms of an A.P. are in G.P., then p-q,q-r,r-s are in
- If the sum of the series 1+ 3x+ 9 x^2 + 27 x^3 + is a finite number, then
- If x,y,z are p^ th ,q^ th and r^ th terms respectively, of an A.P. and also of a G.P., then x^ y-z y^ z-x z^ x-y is equal to
- The sum of the series 1^2+1+2^2+2+3^2+3+ +n^2+n is
- The set of all possible values of x for which 13 is the A.M. of 5^ 1+x and 5^ 1-x , is
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