(a) Find the sum of the Arithmetic Progression (AP) 1, 3, 5,..., 101.

(b) Out of the 95 travellers interviewed, 7 travelled by bus and train only, 3 by train and car only and 8 travelled by all 3 means of transport. The number, x, of travellerswho travelled by bus only was equal to the number who travelled by bus and car only. If 47 people travelled by bus and 30 by train :

(i) represent this information in a Venn diagram;

(ii) calculate the 

(1) value of x ; (2) number who travelled by at least two means.

infinitehoaxx

3 months ago

No answer for question 6a is given by Myschool yet.

Sn = n/2 (a + l) ......... eqn(1)
a = first term = 1
l = last term = 101
n = nth term of the last = ?
d = difference in consecutive terms = 3 - 1 = 2

Using Tn = a + (n - 1)d, we can find the nth term of the last
Tn = 101
101 = 1 + (n - 1)2
101 = 1 + 2n - 2
101 = 2n - 1
101 + 1 = 2n
2n = 102
n = 102/2 = 51

Plotting the value of n into eqn (1), we get
Sn = n/2 (a + l)
S_51 = 51/2 (1 + 101)
= 51/2 (102)
= 51 * 102/2
= 51 * 51
= 2601

Therefore, the sum of the arithmetic progression (A.P.) is 2601