Sequence and Series questions
1035 published questions with worked solutions.
- Let _ n=1 ^ n r^ 4 =f(n). Then _ r=1 ^ n (2r-1)^ 4 is equal to
- If 2 ^ n P_1, ^ n P_2, ^ n P_3 are three consecutive terms of an AP then they are
- In a GP the product of the first four terms is 4 and the second term is the reciprocal of the fourth term. The sum of the GP up...
- If _ k=1 ^ n ( _ m=1 ^ k m^ 2 )=an^ 4 +bn^ 3 +cn^ 2 +dn+e then
- If a,b,c,d are four positive numbers then
- Let f(x)= 1-x^ n+1 1-x and g(x)=1- 2x+ 3 x^2 - +(-1)^n n+1 x^n . Then the constant term in f'(x) g(x) is equal to
- Let a,x,b be in AP; a,y,b be in GP and a,z,b be in HP. If x=y+2 and a=5z then
- Three positive numbers form a GP. If the middle number is increased by 8, the three numbers form an AP. If the last number is...
- If a,b,c are in GP and a,p,q are in AP such that 2a, b+p, c+q are in GP then the common difference of the AP is
- If x,y,z are positive numbers in AP then
- The numbers 1, 4, 16 can be three terms (not necessarily consecutive) of
- If x is a real number such that x(x^2+1), (- 12 )x^2, 6 are three consecutive terms of an AP then the next two consecutive term...
- If , are roots of 375x^2-25x-2=0 and s_n= ^n+ ^n then _ n _ r=1 ^ n s_r is
- If a, b, c are in HP then the expression a(b-c)x^2+b(c-a)x+c(a-b)
- Let A, G and H be the AM, GM and HM of two positive numbers a and b. The quadratic equation whose roots are A and H is
- Let A, G and H are the AM, GM and HM respectively of two unequal positive integers. Then the equation Ax^2-|G|x-H=0 has
- The cubic equation whose roots are the AM, GM and HM of the roots of x^2-2px+q^2=0 is
- If x, y, z are three consecutive terms of a GP, where x>0 and the common ratio is r, then the inequality z+3x>4y holds for
- If a,b,c are three natural numbers in AP and a+b+c=21 then the possible number of values of the ordered triplet (a,b,c) is
- If ^nC_4, ^nC_5 and ^nC_6 are in AP then n is
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