Question

find the sum without actually adding the following odd numbers
1. 1+3+5+7+_ _ _ +35
2. the first 99 odd numbers

Answer 1

Solution

(i) 1 + 5 + 7 + ..... + 35

→ 35 = 1 + (n - 1)(2)

→ 34 = 2(n - 1)

→ 17 = n - 1

→ 18 = n

S18 = 18/2 × [2(1) + (18 - 1)(2)]

→ 9 × [2 + 34]

→ 9 × [36]

→ 324

(ii) S99 = 99/2 × [2(1) + (99 - 1)(2)]

→ 99/2 × [2 + 196]

→ 99/2 × 198

→ 99 × 99

→ 9801

Answer for (i) 324 and (ii) 9801