(i) The first 15 multiples of 8
a = 8, d = 8
S15 = \(\frac{15}{2}\)[2(8) + 14(8)]
= 15[ 8 + 56] = 15[64]
= 960
(ii) The first 40 positive integers divisible by (a) 3 (b) 5 (c) 6.
(a) a = 3, d = 3
\(S_{40} = \frac{40}{2}\)[2(a) + 39(d)]
= 20[2(3) + 39(3)]
= 60 (41)
= 2460
(b) a = 6, d = 5
\(S_{40} = \frac{40}{2}\)[2(5) + 39(5)]
= 100 [41]
= 4100
(iii) All 3 – digit natural numbers which are divisible by 13.
a = 6, d = 6
\(S_{40} = \frac{40}{2}\)[2(6) + 39(6)]
= 120 (41) = 4920
(iv) All 3 – digit natural numbers, which are multiples of 11.
a = 110, d = 11, l = 990
= 8910 [1 + 4]
= 44550
