Sequence And Series | Mathematics | NDA Previous Year Questions

If the nth term of an AP is $${{3 + n} \over 4}$$, then the sum of first 105 terms is

If p, q, r are in one geometric progression and a, b, c are in another geometric progression, then ap, bq, cr are in

What is the sum of n terms of the series $$\sqrt 2 + \sqrt 8 + \sqrt {18} + \sqrt {32} + ...$$?

What is the greatest value of the positive integer n satisfying the condition?

$$1 + {1 \over 2} + {1 \over 4} + {1 \over 8} + .... + {1 \over {{2^{n - 1}}}} < 2 - {1 \over {1000}}$$

How many geometric progressions is/are possible containing 27, 8 and 12 as three of its/their terms?

What is the value of ab?

What is the value of xyz?

What is the value of pqr?

What is the common difference of the AP, so that the product of the first, fourth and fifth terms is greatest?

What is the first term of the AP, so that the product of the first, fourth and fifth terms is greatest?

How many possible values can n have?

What is the largest interior angle of the polygon?

If $${x^{\ln \left( {{y \over z}} \right)}}.{y^{\ln {{(xz)}^2}}}.{z^{\ln \left( {{x \over y}} \right)}} = {y^{4\,\ln \,y}}$$ for any x > 1, y > 1 and z > 1, then which one of the following is correct?

Which one of the following is correct?

x, y and z are

NDA 2016 Paper 1

Which one of the following is correct?

xy, yz and zx are

NDA 2016 Paper 1

The value of the product $${6^{{1 \over 2}}} \times {6^{{1 \over 4}}} \times {6^{{1 \over 8}}} \times {6^{{1 \over {16}}}} \times ....$$ up to infinite terms is

A person is to count 4500 notes. Let a_n denote the number of notes he counts in the n^th minute.

If a₁ = a₂ = a₃ = ...... = a₁₀ = 150, and a₁₀, a₁₁, a₁₂, ..... are in AP with the common difference $$-$$2, then the time taken by him to count all the notes is

If $$y = x + {x^2} + {x^3} + ...$$ up to infinite terms where x < 1, then which one of the following is correct?

The value of $${1 \over {{{\log }_3}e}} + {1 \over {{{\log }_3}{e^2}}} + {1 \over {{{\log }_3}{e^4}}} + ......$$ up to infinite terms is

If $$1.3 + {2.3^2} + {3.3^3} + ... + n{.3^n} = {{(2n - 1){3^a} + b} \over 4}$$, then a and b are respectively.

If $${S_n} = nP + {{n(n - 1)Q} \over 2}$$, where, S_n denotes the sum of the first n terms of an AP, then the common difference is

What is the sum of the series 0.3 + 0.33 + 0.333 + ..... n terms?

If the sum of m terms of an AP is n and the sum of n terms is m, then the sum of (m + n) terms is

The fifth term of an AP of n terms, whose sum is n² $$-$$ 2n, is

The sum of all the two-digit odd numbers is

The sum of the first n terms of the series $${1 \over 2} + {3 \over 4} + {7 \over 8} + {{15} \over {16}} + ....$$ is equal to

If an infinite GP has the first term x and the sum 5, then which one of the following is correct?

The sum of the series $$3 - 1 + {1 \over 3} - {1 \over 9} + .......$$ is equal to

Let T_r be the r^th term of an AP for r = 1, 2, 3, ...... If for some distinct positive integers m and n we have T_m = 1 / n and T_n = 1 / m, then what is T_mn equal to?

If the second term of a GP is 2 and the sum of its infinite terms is 8, then the GP is

If a, b, c are in AP or GP or HP, then $${{a - b} \over {b - c}}$$ is equal to

If the ratio of AM and GM of two positive numbers a and b is 5 : 3, then a : b is equal to

If $$x = 1 - y + {y^2} - {y^3}....$$ up to infinite terms, where $$\left| y \right| < 1$$, then which one of the following is correct?

What is the sum of all two-digit numbers, which when divided by 3 leave 2 as the remainder?

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

If $$x,{3 \over 2},z$$ are in AP, x, 3, z are in GP, then which one of the following will be in HP?

If 3rd, 8th and 13th terms of a GP are p, q and r respectively, then which one of the following is correct?

Let S_n be the sum of the first n terms of an AP. If S_2n = 3n + 14n², then what is the common difference?

How many two-digit numbers are divisible by 4?

If the sum of first n terms of a series is (n + 12), then what is its third term?

Let a, b, c be in AP and k $$\ne$$ 0 be a real number. Which of the following are correct?

1. ka, kb, kc are in AP

2. k $$-$$ a, k $$-$$ b, k $$-$$ c are in AP

3. $${a \over k}$$, $${b \over k}$$, $${c \over k}$$ are in AP

Select the correct answer using the code given below.

Let m and n(m < n) be the roots of the equation x² $$-$$ 16x + 39 = 0. If four terms p, q, r and s are inserted between m and n to form an AP, then what is the value of p + q + r + s?

A geometric progression (GP) consists of 200 terms. If the sum of odd terms of the GP is m, and the sum of even terms of the GP is n, then what is its common ratio?

What is the value of 1 $$-$$ 2 + 3 $$-$$ 4 + 5 $$-$$ ......... + 101?

What is the nth term of the sequence 25, $$-$$ 125, 625, $$-$$ 3125, ........ ?

The numbers 1, 5 and 25 can be three terms (not necessarily consecutive) of

The sum of (p + q) th and (p $$-$$ q)th terms of an AP is equal to

What is the fourth term of an AP of n terms whos sum is n(n + 1)?

If p times the pth term of an AP is equal to q times the qth term (p ≠ q), then what is the (p + q)th term equal to?

Let p = ln(x), q = ln(x³) and r = ln(x⁵), where x > 1. Which of the following statements is/are correct?

I. p, q and r are in AP.

Il. p, q and r can never be in GP.

Select the answer using the code given below.

Let x >1, y >1, z >1 be in GP. Then $\rm \frac{1}{1+ln x}, \frac{1}{1+lny}, \frac{1}{1+\ln z}$ are

If the sum of the first n terms of a series is n(2n+1), then what is the nth term?

In an AP, the ratio of the sum of the first p terms to the sum of the first q terms is p² : q². Which one of the following is correct?

What is the common difference?

What is the sum of all five terms?

The mean of n observations

1, 4, 9, 16 ...., n² is 130. What is the value of n?

NDA Mathematics 21 April 2024

What is the remainder when $2^{120}$ is divided by 7?

If $a, b, c$ are in AP; $b, c, d$ are in GP; $c, d, e$ are in HP, then which of the following is/are correct?

1. $a, c,$ and $e$ are in GP

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

Select the correct answer using the code given below:

NDA Mathematics 21 April 2024

If $a, b, c$ are in HP, then what is $\frac{1}{b-a} + \frac{1}{b-c}$ equal to?

1. $\frac{2}{b}$

2. $\frac{1}{a} + \frac{1}{c}$

3. $\frac{1}{2} \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)$

Select the correct answer using the code given below:

NDA Mathematics 21 April 2024

If the nth term of a sequence is $\frac{2 n+5}{7}$, then what is the sum of its first 140 terms?

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 x, y, z are in GP, then which of the following is/are correct?

1. ln(3x), ln(3y), ln(3z) are in AP

2. xyz + ln(x), xyz + ln(y), xyz + ln(z) are in HP

Select the correct answer using the code given below.

If log102, log10(2x - 1), log10(2x + 3) are in AP, then what is x equal to?

If p = (1111 ... up to n digits), then what is the value of 9p² + p?

If a_n = n(n!), then what is a₁ + a₂ + a₃ +...+ a₁₀ equal to?

$\frac{1}{b+c}, \frac{1}{c+a},\frac{1}{a+b}$ are in HP, then which of the following is/are correct?

1. a, b, c are in AP

2. (b + c)², (c + a)², (a + b)²are in GP. Select the correct answer using the code given below.

Let p, q and 3 be respectively the first, third and fifth terms of an AP. Let d be the common difference. If the product (pq) is minimum, then what is the value of d?

Let S_k denote the sum of first k terms of an AP. What is $\rm \frac{S_{30}}{S_{20}-S_{10}}$ equal to?

If the harmonic mean of 60 and x is 48, then what is the value of x?

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

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