Question

1 + 2a + 3 + 4a + 5 + 6a + ...... + 97 + 98a + 99 + 100a = 0 What does a equal?

Answer 1

a = -50/51

Explanation:

1 + 2a + 3 + 4a + 5 + 6a + ...... + 97 + 98a + 99 + 100a = 0

1 + 3 + 5 + ... + 99 + 2a + 4a + ... + 98a + 100a = 0 Eq. 1

99 + 97 + 95 + ... + 1 + 98a + 96a + ... + 4a + 2a = 0 Eq. 2

Add Eq. 1 and Eq. 2

100 + 100 + ... + 100 + 102a + 102a + ... 102a = 0

50(100)/2 + 50(102a)/2 = 0

2500 + 2550a = 0

2550a = -2500

a = -2500/2550

a = -250/255

a = -50/51