Sequence and Series questions
1035 published questions with worked solutions.
- If a_1 = 1 and a_n = n a_ n-1 for all positive integer n 2, then a_5 is equal to
- The sum to n terms of the series 1^3 + 3^3 + 5^3 + is
- The nth term of the series 4 + 14 + 30 + 52 + 80 + 114 + is
- 3 + 13 + 29 + 51 + 79 + to n terms =
- The sum of n terms of the series 1 + (1+a) + (1+a+a^2) + (1+a+a^2+a^3) + , is
- For all n N, n
- The nth terms of the series 3 + 7 + 13 + 21 + is
- If a, b, c > 0, the minimum value of a b+c + b c+a + c a+b is
- If a, b, c > 0 and if abc = 1, then the value of a + b + c + ab + bc + ca lies in the interval
- If the product of n positive numbers is n^n, then their sum is
- If a, b, c are positive real numbers such that a + b + c = p then, which of the following is true?
- If a_1, a_2, a_3 be any positive real numbers, then which of the following statements is not true
- If x,y,z are in GP and a^x=b^y=c^z, then
- If the roots of the equation 4x^3-12x^2+11x+k=0 are in arithmetic progression, then k is equal to
- If the roots of x^3-3x^2-6x+8=0 are in arithmetic progression, then the roots of the equation are
- If 1 is any nth root of unity, then S=1+3 +5 ^2+ upon n terms, is equal to
- The harmonic mean of the roots of the equation (5+ 2 )x^2- (4+ 5 )x+8+2 5=0 is
- If and are the roots of x^2-x-1=0 and A_n= ^n+ ^n, then AM of A_ n-1 and A_n is
- If the roots of the equation 8x^3-14x^2+7x-1=0 are in GP, then the roots are
- Given and are the roots of the quadratic equation x^2-4x+k=0 (k 0). If , ^2+ ^2 , ^3+ ^3 are in geometric progression, then the...
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