MOCK TEST ON ARITHMETIC AND GEOMETRIC SEQUENCES AND SERIES

Problem 1 :

Which term of the AP

3/√7, 4/√7, 5/√7, ............ is 17/√7 ?

Solution

Problem 2 :

Divide 69 into three parts which are in A.P and are such that the product of the first two parts is 483.

Solution

Problem 3 :

Insert 4 arithmetic means between 4 and 324.

Solution

Problem 4 :

If the p^th term of an A.P is q and q^th term is p the value of the r^th term is 

(a)  p - q - r     (b) p + q - r    (c) p + q + r    (d)  None

Solution

Problem 5 :

The sum of a series in A.P is 72 the first term is 17 and the common difference -2, the number of terms is 

(a)  6     (b)  12     (c)  6 or 12     (d) None

Solution

Problem 6 :

The sum of all natural numbers between 500 and 1000, which are divisible by 13 is

(a)  28400     (b)  28405     (c)  28410     (d) None

Solution

Problem 7 :

If the 10^th term of an A.P. is twice the 4^th term, and the 23^rd term is 'k' times the 8^th term, then the value of 'k' is

(a) 2.5      (b) 3        (c) 3.5        (d) 4

Solution

Problem 8 :

The sum of the A.M. and G.M. of two positive numbers is equal to the difference between the numbers. The numbers are in the ratio.

(a) 1 : 3       (b) 1 : 6       (c) 9 : 1        (d) 1 : 12

Solution

Problem 1 :

t₁₂ of the series -128, 64, -32, ................ is

(a) -1/16    (b) 16     (c)  1/16     (d) None

Solution

Problem 2 :

The last term of the series

x², x, 1.................. to 31 terms is 

(a) x²⁸    (b) 1/x     (c)  1/x²⁸     (d) None

Solution

Problem 3 :

The sum of the series 

243, 81, 27, ............. to 8 terms.

(a) 36    (b) 36  13/30     (c)  36  1/9     (d) None

Solution

Problem 4 :

The second terms of a G.P is 24 and the fifth term is 81. The series is

(a) 16, 36, 24, 54,....         (b)  24, 36, 53, .......

(c)  16, 24, 36, 54, ........    (d)  None

Solution

Problem 5 :

The sum of n terms of the series 4 + 44 + 444 + .......... is

(a) (4/9)[(10/9) (10ⁿ - 1) - n]         (b)  (10/9)(10ⁿ - 1) - n 

(c) 4/9(10ⁿ - 1) - n         (d)  None

Solution

Problem 6 :

The sum of first 20 terms of a G.P is 244 times the sum of the first 10 terms. The common ratio is 

(a) ±√3         (b)  ±3       (c)  √3       (d)  None

Solution

Problem 7 :

The product of 3 numbers in GP is 729 and the sum of squares is 819, the numbers are 

(a) 9, 3, 27         (b)  27, 3, 9       (c)  3, 9, 27       (d)  None

Solution

Problem 8 :

Four geometric means between 4 and 972 are 

(a) 12, 36, 108, 324         (b)  12, 24, 108, 320

(c)  10, 36, 108, 320          (d)  None

Solution

Problem 9 :

Find the first term and common difference and the n^th term of the sequence given the following conditions 

second term is 16, 5th term is 1/4

Solution