Find the middle term(s) of an A.P. 9, 15, 21, 27,…,183.

Find the middle term(s) of an A.P. 9, 15, 21, 27,…,183.

Solution :

In order to find the middle term of the sequence, first we have to know how many terms are in the given sequence.

n = [(l - a)d] + 1

a = 9, d = 15 - 9  ==> 6 and l = 183

n = [(183 - 9)/6] + 1

 n = (174 / 6) + 1

n = 29 + 1  = 30

n = 30(even)

middle terms are (n/2)th term and [(n/2) + 1]th term

15th term  = a + 14d =  9 + 14(6) =  93

16th term  = a + 15d =  9 + 15(6) =  99

Check whether the following sequences are in A.P. (iii) 9, 13, 17, 21, 25,...

Check whether the following sequences are in A.P.

(iii) 9, 13, 17, 21, 25,...

Solution :

d = t2 - t1 d = 13 - 9 d  = 4

d = t3 - t2 d = 17 - 13 d  = 4

The given sequence is an arithmetic progression.

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