Sequences and Series - 2 - JEE MCQ

If A.M., G.M. and H.M. of first and last terms of the series 100, 101, 102,…. n –1, n are the terms of the series it self then the value of n is (100 < n ≤ 500 )

If (1 – y) (1 + 2x + 4x² + 8x³ + 16x⁴ + 32x5) = 1 – y6, (y ≠ 1), then a value y/x is -

11² + 12² + 13² +…..20² is equal to

If | a | <1 & | b | < 1 then sum of the series a (a + b) + a³² (a²+ b²) + a³ (a³+ b³) + ….. up to ∞ is

Consider an infinite G.P. with first term a and common ratio r. Its sum is 4 and the second term is 3/4, then

Let S₁, S₂,… be squares such that for each n ≥ 1, the length of a side of S_n equals the length of a diagonal of S_n+1. If the length of a side of S₁ is 10 cm, then the smallest value of n for which Area (S_n) < 1 is -

Let a, b be the roots of x² –3x + p = 0 and let c, d be the roots of x² –12x + q = 0, where a, b, c, d form an increasing G.P. Then the ratio of q + p : q – p is equal to

Sum of the series .5 + .55 + .555 + ………. upto n terms is

Sum upto 20 terms 1.3² + 2.5² + 3.7² + ……….. =

Suppose a, b, c are in A.P. and a², b², c² are in G.P. If a < b < c and a + b + c =3/2, then the value of a is -

If the sixth term of an A.P. is equal to 2. the value of the common difference of the A.P. which makes the product a₁ a₄ a₅ the greatest is 

(the ith term is denoted by a)

If x, y, z are positive nos. minimum value of  x^{lny –lnz} + y^lnz–lnx + z^{lnx –lny} is –