If first and last terms ofanAP. are 3 and 18 and the sum of its terms is 84, then number of terms will be ______.

1

(a)

5

(b)

6

(c)

7

(d)

8

If the sum of n terms of an AP. is 4n² + 7n, then its nth term is ______.

1

(a)

8n -3

(b)

8n + 3

(c)

3n - 8

(d)

None of these

If Sn denote the sum of n terms of an  AP. whose first term is a and common difference is d given by is d given by d = S_n - kS_n-1 + S_n-2 then K is equal to ______.

1

(a)

5

(b)

2

(c)

3

(d)

4

If the first, 'second and last term of an AP. are a, band 2a respectively then its sum is equal to ______.

1

(a)

\(\frac { b }{ 2(b-a) } \)

(b)

\(\frac { a }{ 3(b-a) } \)

(c)

\(\frac { 3ab }{ 2(b-a) } \)

(d)

\(\frac { 2ab }{ 3(b-a) } \)

If the first term of an AP. is 5 and common difference is - 3 then sum of its 60 terms is equal to ______.

1

(a)

-1050

(b)

-5010

(c)

3010

(d)

None of these

If a, b, c are in G.P. and \({ a }^{ \frac { 1 }{ x } }={ b }^{ \frac { 1 }{ y } }={ c }^{ \frac { 1 }{ z } }\), then xyz are in ______.

1

(a)

A.P

(b)

G.P

(c)

None of these

The three geometric means between the numbers 1 and 81 are ______.

1

(a)

3, 6 and 18

(b)

3, 9 and 27

(c)

3, 6 and 27

(d)

None of these

In a G.P. if the (m + n)^th terms is p and (m - n)^th terms is q then its mth terms is ______.

1

(a)

-1

(b)

pq

(c)

\(\sqrt { pq } \)

(d)

\(\frac { 1 }{ 2 } \left( p+q \right) \)

If the sum of first n even natural numbers is equal to m times the sum of first n is odd natural numbers then m is equal to ______.

1

(a)

\(\frac { n-1 }{ n } \)

(b)

\(\frac { n+1 }{ n } \)

(c)

\(\frac { 2n+1 }{ n } \)

(d)

None of these

Sum of n terms of ,the series \(\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +\sqrt { 32 } +\)..... is ______.

1

(a)

\(\left[ \frac { n(n+1) }{ 2 } \right] ^{ 2 }\)

(b)

n² (n+3)

(c)

\(\frac { n(n+1) }{ \sqrt { 2 } } \)

(d)

2

The sum to infinity of \(\frac{1}{3}+\frac{3}{9}+\frac{5}{27}+\frac{7}{81}+...+\infty\) is ______.

1

(a)

2

(b)

1

(c)

0

(d)

3

The sum of the square of (n - 1) natural numbers is ______.

1

(a)

\(\frac{n(n+1)(2n+1)}{6}\)

(b)

\(\frac{n(n-1)(2n-1)}{6}\)

(c)

\(\frac{(n+1)(n-1)(n-2)}{6}\)

(d)

None

The seen to infinity of the series \(1+2.\frac{1}{2}+3.\frac{1}{2^2}+4.\frac{1}{2^3}+...+\infty\) ______.

1

(a)

4

(b)

5

(c)

1

(d)

None

The sum of infinity of the G.P. a, ar, ar², ar³, ...... \(\infty\) is ______.

1

(a)

\(\frac{a-1}{1-r}\)

(b)

\(\frac{a}{1-r}\)

(c)

\(\frac{2a}{1-r}\)

(d)

\(\frac{a}{1-r^2}\)