Ch1 Review Problem

Compute 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99.

Answer explanation

We pair the smallest number with the largest, the second smallest with the second largest, and so on:

90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99

= (90 + 99) + (91 + 98) + (92 + 97) + (93 + 96) + (94 + 95)

= 189 + 189 + 189 + 189 + 189

= 5 × 189

= 945.

Compute

3(101 + 103 + 105 + 107 + 109 + 111 + 113 + 115 + 117 + 119).

Answer explanation

Subtraction is addition of a negation, so

Answer explanation

Let’s pair up the first and second numbers, the third and fourth numbers, and so on:

1 - 3 + 5 - 7 + 9 - 11 + 13 - 15 + 17 - 19 + 21 - 23 + 25

= (1 - 3) + (5 - 7) + (9 - 11) + (13 - 15) + (17 - 19) + (21 - 23) + 25

= (-2) + (-2) + (-2) + (-2) + (-2) + (-2) + 25

= 6(-2) + 25

= -12 + 25

= 13