Question

Write four arithmetic sequences with 100 as the sum of the first four terms.

Answer 1

If the first four terms are

x – 3d, x – d, x + d, x + 3d

x – 3d + x – d + x + d + x + 3d = 100 

4x = 100 

x = 25 

i. If d = 1 

The arithmetic sequence is 22, 24, 26, 28 

ii. If d = 2 

The arithmetic sequence is 19, 23, 27, 31 

iii. If d = 3 

The arithmetic sequence is 16, 22, 28, 34 

iv. If d = 4 

The arithmetic sequence is 13, 21, 29, 37