F6 Arithmetic Sequences 01q1

2.
(a)
(i) The first term, T1 = a = 6 x 1 = 6
(ii) The common difference, d = Tn - Tn-1 = 6n - 6(n - 1) = 6
(iii) T4 = 6 x 4 = 24

(b)
(i) The first term, T1 = a = 4 - 7 x 1 = -3
(ii) The common difference, d = Tn - Tn-1 = (4 - 7n) - [4 -7(n-1)] = -7
(iii) T4 = 4 - 7 x 4 = -24

(c)
(i) The first term, T1 = a = (1/2)(1 - 1) = 0
(ii) The common difference, d = Tn - Tn-1 = (1/2)(n - 1) -(1/2)[(n - 1) - 1] = 1/2
(iii) T4 = (1/2)(4 - 1) = 3/2


*****
16.
(a)(i)
T3 = a + 2d
16 + 2d = 42
d = 13

The number to be inserted = a + d = 16 + 13 = 29

(a)(ii)
m - 16 = 42 - m
2m = 58
m = 29

(b)
(ii) is more convenient.