Progression (Sequence and Series) Questions

Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 12 + 2·22 + 32 + 2·42 + 52 + 2·62 + ....... If B - 2A = 100λ, then λ is equal...

The value of cot cot-1 is

Let Then Sn can take value(s)

Four fair dice D1, D2, D3 and D4, each having six faces numbered 1, 2, 3, 4, 5, and 6, are rolledsimultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is...

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression sin 2C +...

The third term of a geometric progression is $4$. The product of the first five terms is:

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

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the ...

The change in the value of g at a height ′h′ above the surface of the earth is the same as at a depth ′d′ below the surface of earth. When both ′d′ and ′h&#82...

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

The sum of the series 20C0 20C1 + 20C2 - 20C3 + .... - .... + 20C10 is...

The sum of the series upto infinity is

If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

If the letters of word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

If x is so small that x3 and higher powers of x may be neglected, then may be approximated as...

If x = where a, b, c are in A.P. and |a|

If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in

Let a, b and c be distinct non-negative numbers. If the vectors and lie in a plane, then c is...

The sum of the series ad inf. is

The sum of the first n terms of the series 12 + 2 . 22 + 32 + 2 . 42 + 52 + 2 . 62 + ... is when n is even. When n is odd the sum is...