Sequence and Series questions
1035 published questions with worked solutions.
- If x,a,b,c are real and (x-a+b)^2+(x-b+c)^2=0, then a,b,c are in
- The roots , and of an equation x^3-3ax^2+3bx-c=0 are in H.P. Then,
- If the roots of x^3-12x^2+39x-28=0 are in A.P., then their common difference is
- If , are roots of the equation 375x^2-25x-2=0 and S_n= ^n+ ^n, then _ n _ r=1 ^nS_r is equal to
- If the roots of the equation x^3+bx^2+3x-1=0 form a non-decreasing H.P., then
- If A is the A.M. of the roots of the equation x^2-2ax+b=0 and G is the G.M. of the roots of the equation x^2-2bx+a^2=0, then
- Let a₁, a₂, a₃, … be an A.P. and g₁ = a₁, g₂, g₃, … be an increasing G.P. If a₁ = a₂ + g₂ = 1 and a₃ + g₃ = 4, then a₁₀ + g₅ is...
- The sum 1^3 1 + 1^3+2^3 1+3 + 1^3+2^3+3^3 1+3+5 + up to 8 terms, is:
- Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of...
- If _ k=1 ^ n a_k = 6n^3, then _ k=1 ^ 6 ( a_ k+1 - a_k 36 )^2 is equal to _______.
- The first term of an A.P. of 30 non-negative terms is 10 3. If the sum of this A.P. is the cube of its last term, then its common...
- Let α = 1/4+1/8+1/16+… ∞ and β = 1/3+1/9+1/27+… ∞. Then the value of (0.2)^ _ 5 + (0.04)^ _5 is equal to:
- Let A₁,A₂,A₃,…,A₃₉ be 39 arithmetic means between the numbers 59 and 159. Then the mean of A₂₅, A₂₈, A₃₁ and A₃₆ is equal to:
- Let the sum of the first n terms of an A.P. be 3n²+5n. Then the sum of squares of the first 10 terms of the A.P. is:
- _ n=1 ^ 10 ( 528 n(n+1)(n+2) ) is equal to:
- The sum 1+ 12(1^2+2^2)+ 13(1^2+2^2+3^2)+ upto 10 terms is equal to:
- The value of 1³−2³+3³−…+15³ is:
- The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P....
- Let α = 3 + 4 + 8 + 9 + 13 + 14 + … upto 40 terms. If ( )^ 1020 is a root of the equation x² + x − 2 = 0, β ∈ (0, π/2), then...
- Let a, ar, ar², ........ be an infinite G.P. If _ n=0 ^ ar^n = 57 and _ n=0 ^ a^3r^ 3n = 9747, then a + 18r is equal to :
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