Question

The sum of the first five terms of an arithmetic sequence is 90 less than the sum of the next five terms. What is the absolute difference between two consecutive terms of this sequence? Express your answer as a common fraction.

Answer 1

18/5

Explanation:

let the first term of arithmetic sequence = a and the common difference =d

The first term = a

second term = a + d

third term = a + 2d

fourth term = a + 3d

fifth term = a + 4d

Therefore, the sum of the first five terms = a + (a+d) +(a+2d)+(a+3d)+(a+4d)=5a +10d

The next five terms are

sixth term=a+5d

seventh term=a+6d

eight term=a+7d

ninth term=a+8d

tenth term=a+9d

The sum of the next five terms above=(a+5d)+(a+6d)+(a+7d)+(a+8d)+(a+9d)=5a+35d

The sum of the first five terms is 90 less than the sum of the next five terms

Therefore, 5a+9d+90=5a+35d

90=35d-10d=25d

d=90/25=18/5

Therefore the absolute difference between consecutive terms =18/5