Find the next three terms of the following sequence. (ii) 5, 1,-3,…

Find the next three terms of the following sequence.

(ii) 5, 1,-3,…

Solution :

Pattern :

By subtracting 4 from the 1st term, we get second term. By subtracting 4 from 2nd term, we get 3rd term.

4th term  = -3 - 4  = -7

5th term  = -7 - 4  = -11

6th term  = -11 - 4  = -15

Hence the next three terms are -7, -11, -15.

Let A = {-5,-3,-2,-1} B = {-2,-1,0} and C = {-6,-4,-2}. Find A\(B\C) and (A\B)\C. What can we conclude about set difference operation?

Question 10

Let A = {-5,-3,-2,-1} B = {-2,-1,0} and C = {-6,-4,-2}. Find A\(B\C) and (A\B)\C. What can we conclude about set difference operation?

Solution:

A = {-5,-3,-2,-1} B = {-2,-1,0} and C = {-6,-4,-2}

L.H.S

A\(B\C)

(B\C) = {-2,-1,0} \ {-6,-4,-2}

    = {-1,0}

A\(B\C) = {-5,-3,-2,-1} \ {-1,0}

       = {-5,-3,-2} ---- (1)

R.H.S

(A\B)\C

(A\B) = {-5,-3,-2,-1} \ {-2,-1,0}

    = {-5,-3}

(A\B)\C = {-5,-3} \ {-6,-4,-2}

       = {-5,-3}  -----(2)

(1) ≠ (2)

A\(B\C) ≠ (A\B)\C