Find x, y and z, given that the numbers x, 10, y, 24, z are in A.P.

Find x, y and z, given that the numbers x, 10, y, 24, z are in A.P.

Solution :

Since the given sequence is an arithmetic progression,

t2 - t1  = 10 - x  ---(1)

t3 - t2  = y - 10 ---(2)

t4 - t3  = 24 - y ---(3)

t5 - t4  = z - 24 ---(4)

(1)  = (2) 10 - x  = y - 10 x + y  = 20

(2) = (3) y - 10  = 24 - y y + y  = 24 + 10 2y  = 34 y  = 17

By applying the value of y in x + y  = 20

x + 17  = 20

x  = 3

(3)  = (4)

24 - y  = z - 24

y + z  = 24 + 24

y + z  = 48

17 + z  = 48

z  = 31

Hence the values of x, y and z are 3, 17, 31 respectively.

Find the nth term of the following sequences (i) 2, 5, 10, 17,...

Find the nth term of the following sequences

(i) 2, 5, 10, 17,...

Solution :

(1 + 1), (4 + 1), (9 + 1), (16 + 1),...

(12 + 1), (22 + 1), (32 + 1), (42 + 1),...

nth term of the sequence  :

an  = n2 + 1

Let f : A -> B be a function defined by f (x) = (x/2) - 1 where A = {2, 4, 6, 10, 12}, B = {0, 1, 2, 4, 5, 9} .

Let f : A -> B be a function defined by f (x) =  (x/2) - 1 where A = {2, 4, 6, 10, 12}, B = {0, 1, 2, 4, 5, 9} .

Represent f by

(i) set of ordered pairs; (ii) a table; (iii) an arrow diagram; (iv) a graph

Solution :

(i) set of ordered pairs

f (x) =  (x/2) - 1

Set of ordered pairs  = {(2, 0) (4, 1) (6, 2) (10, 4) (12, 5)}

(ii) a table

(iii) an arrow diagram;

(iv) a graph

For A = {5,10,15,20} B = {6,10,12,18,24} and C ={7,10,12,14,21,28} verify whether A\ (B\C) = (A\B)\C. Justify your answer.

Question 9

For A = {5,10,15,20} B = {6,10,12,18,24} and C ={7,10,12,14,21,28} verify whether A\ (B\C) = (A\B)\C. Justify your answer.

Solution:

A = {5,10,15,20}

B = {6,10,12,18,24}

C = {7,10,12,14,21,28}

L.H.S

A\(B\C)

(B\C) = {6,10,12,18,24} \ {7,10,12,14,21,28}

    = {6,18,24}

A\(B\C) = {5,10,15,20} \ {6,18,24}

       = {5,10,15,20}  ---(1)

(A\B) = {5,10,15,20}\{6,10,12,18,24}

    = {5,15,20}

(A\B)\C = {5,15,20} \ {7,10,12,14,21,28}

       = {5,15,20}   --- (2)

A\ (B\C) ≠ (A\B)\C