Sequences and S...

The sum of first 12 terms of the series. \(1^{2}+\left(1^{2}+2^{2}\right)+\left(1^{2}+2^{2}+3^{2}\right)+.......\) is:

If \(a, b, c\) are in G.P., then the equations \(a x^{2}+2 b x+c=0\) and \(d x^{2}+2 e x+f\) \(=0\) have a common root if \(\frac{d }{ a} , \frac{e }{ b} ,\frac{ f }{ c}\) are in:

If \(\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\) are in AP, then \(\left(\frac{1}{a}+\frac{1}{b}-\frac{1}{c}\right)\left(\frac{1}{b}+\frac{1}{c}-\frac{1}{a}\right)\) is equal to:

Find the sum of all numbers divisible by 6 in between 100 to 400.

The sum of the first \(n\) terms of the series \(\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+\ldots\) is equal to:

If \(\frac{2 }{ 3}, K , \frac{5 }{ 8}\) are in AP, then value of \(K\) is:

If the product of three terms in a GP is 27. Find its middle term.

The product of three numbers in AP is 224 and the largest number is 7 times the smallest. Find the largest number.

Which term of an AP 403, 397, 391 ....... is the first negative term?

The geometric mean and harmonic mean of two non-negative observations are 10 and 8 respectively. Then what is the arithmetic mean of the observations equal to: