Which of the following sequences are in G.P.? (vi) 120,60,30,18,…

Which of the following sequences are in G.P.?

(vi) 120,60,30,18,…

Solution :

First term (a)  = 120, common ratio

r  = t2/t1   =  60/120 r  = 1/2

r  = t2/t1   =  30/60 r = 1/2

Since the common ratios are same, it is geometric sequence.

Find the nth term of the following sequences (iii) 3, 8, 13, 18,...

Find the nth term of the following sequences

(iii) 3, 8, 13, 18,...

Solution :

  =  3, 8, 13, 18,...

we may see the common things followed in each term.

  =  (5 - 2), (10 - 2), (15 - 2), (20 - 2),...

nth term of the sequence is 5n - 2.

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