JEE Advanced Level Test: Sequences And Series- 1 - JEE MCQ

The third term of a G.P. is 4. The product of the first five terms is

If S is the sum of infinity of a G.P. whose first term is `a', then the sum of the first n terms is

The sum of the series  +  +  + ....... +  is

For a sequence {a_n}, a₁ = 2 and . Then  is

a, b be the roots of the equation x^2 – 3x + a = 0 and g, d the roots of x² – 12x + b = 0 and numbers a, b, g, d (in this order) form an increasing G.P., then

If 3 + 1/4 (3 + d) + 1/4² (3 + 2d) + .... + upto ∞ = 8, then the value of d is

The sum  is equal to

In a G.P. of positive terms, any term is equal to the sum of the next two terms. The common ratio of the G.P. is

If  + ...... up to ∞ =, then  + ..... =

Sum of the series S = 1² – 2² + 3² – 4² + ..... – 2002² + 2003² is

If x =, y =, z =where a, b, c are in AP and |a| < 1, |b| < 1, |c| < 1, then x, y, z are in

The sum to n term of the series 1(1!) + 2(2!) + 3(3!) + ....

The sum to 10 terms of the series is

If p is positive, then the sum to infinity of the series,  is

The positive integer n for which 2 × 2² + 3 × 2³ + 4 × 2⁴ + ..... + n × 2ⁿ = 2^{n + 10} is

If x > 0, and log₂ x + log₂  + log₂  + log₂  + log₂  + ....= 4, then x equals

If a, b, c are in A.P. p, q, r are in H.P. and ap, bq, cr are in G.P., then  is equal to

1² + 2² + ......+ n² = 1015, then value of n is

If a and b are p^th and q^th terms of an AP, then the sum of its (p + q) terms is