Sequence And Series · Mathematics · NDA

If (a + b), 2b, (b + c) are in HP, then which one of the following is correct?

Let t1, t2, t3 ... be in GP. What is $\rm \left(t_1 t_3 \ldots t_{21}\right)^{\frac{1}{11}}$ equal to ?

What is a1 + a5 - a10 - a15 - a20 - a25 + a30 + a34 equal to ?

What is $\displaystyle \sum_{n=1}^{34} a_n$ equal to ?

If log_xa, a^x and log_bx are in GP, then what is x equal to ?

If $2^{\frac{1}{c}}, 2^{\frac{b}{a c}}, 2^{\frac{1}{a}}$ are in GP, then which one of the following is correct ?

The first and the second terms of an AP are $\frac{5}{2}$ and $\frac{23}{12}$ respectively. If n^th term is the largest negative term, what is the value of n ?

In an AP, the first term is x and the sum of the first n terms is zero. What is the sum of next m terms ?

p, q, r and s are in AP such that p + s = 8 and qr = 15. What is the difference between largest and smallest numbers ?

If G is the geometric mean of numbers 1, 2, 2², 2³,.....2^n-1, then what is the value of 1 + 2log₂G ?

If H is the harmonic mean of numbers 1, 2, 2², 2³, ......2^n-1 what is n/H equal to ?

Consider the following statements :

1. 2 + 4 + 6 + ........ + 2n = n2 + n

2. The expression n2 + n + 41 always gives a prime number for every natural number n

Which of the above statements is/are correct ?

What is the ratio of the first term of A to that of B ?

What is the ratio of their 10th terms ?

If d is the common difference of A, and D is the common difference of B, then which one of the following is always correct ?

If $\displaystyle\sum_{x=2}^n$f(x) = 2044, then what is the value of n ?

Let x be the mean of squares of first n natural numbers and y be the square of mean of first n natural numbers. If $\frac{\text{x}}{\text{y}} = \frac{55}{42}$, then what is the value of n ?

If a, b, c are in GP where a > 0, b > 0, c > 0, then which of the following are correct?

1. a², b², c² are in GP

2. $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in GP

3. $\sqrt {a}, \sqrt{b}, \sqrt{c} $ are in GP

Select the correct answer using the code given below :

If $\frac{a+b}{2}, b, \frac{b+c}{2}$ are in HP, then which one of the following is correct?

If the sum of the first 9 terms of an AP is equal to sum of the first 11 terms, then what is the sum of the first 20 terms ?

If the 5^th term of an AP is $\frac{1}{10}$ and its 10^th term is $\frac{1}{5},$ then what is the sum of first 50 terms ?

What is the arithmetic mean of 50 terms of an AP with first term 4 and common difference 4 ?

What is the mean of the marks ?

What is the median of the marks?

What is the sum of the deviations measured from the median?

If the first term of an AP is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, then what is the sum of the first ten terms?

Consider the following statements:

1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP.

2. If each term of a GP is divided by same non-zero number, then the resulting sequence is also a GP.

Which of the above statements is/are correct?

If x², x, -8 are in AP, then which one of the following is correct?

The third term of a GP is 3. What is the product of its first five terms?

Let x be the HM and y be the GM of two positive numbers m and n. If 5x = 4y, then which one of the following is correct?

The geometric mean of a set of observations is computed as 10. The geometric mean obtained when each observations x_i is replaced by $\rm 3x_i^4$ is