Class 11 Mathematics: Sequences and Series Worksheet

If the sum of n terms of an A.P. is given by S_n = 3n^2 + 2n, then the common difference of the A.P. is:

If a, b, c are in A.P., b, c, d are in G.P. and c, d, e are in H.P., then a, c, e are in:

The sum of the series 1 / (1 × 2) + 1 / (2 × 3) + 1 / (3 × 4) + ... up to n terms is:

If x, y, z are in G.P. and a^x = b^y = c^z, then:

The sum of the infinite series 1 + x / (1 + x) + x^2 / (1 + x)^2 + ... (for |x| < 1) is:

If the p-th term of an A.P. is q and the q-th term is p, then its (p+q)-th term is ____.

The sum of the series S = 1 + 1/3 + 1/5 + 1/7 + .... up to n terms is a partial sum of a sequence of ____.

If A is the arithmetic mean and G is the geometric mean of two positive numbers a and b, then the quadratic equation whose roots are a and b is x^2 - ____ x + G^2 = 0.

If x = 1 + a + a^2 + ... (infinity) and y = 1 + b + b^2 + ... (infinity) where |a| < 1 and |b| < 1, prove that 1 + ab + a^2b^2 + ... (infinity) = xy / (x + y - 1).

Find the sum of n terms of the series whose nth term is n(n+3).