The first term of a sequence is 20 and the second term is 8. The third term and each term thereafter is the average of the two terms immediately preceding it. What is the value of the first term in the sequence that is not an integer?

12.5

Step-by-step explanation:

Let the first term T1 be a,

second term T2 = a+d where d is the common difference

If the third term and each term thereafter is the average of the two terms immediately preceding it then;

T3 = T2+T1/2

T3 = a+d+a/2

T3 = 2a+d/2

Since the first term of the sequence is 20 and the second term is 8;

a = 20 ... 1

a+d = 8 ... 2

from 2; d = 8-20

d = - 12

T3 = 2 (20) + (-12) / 2

T3 = 40-12/2

T3 = 28/2

T3 = 14 (This value is an integer)

We will proceed to check the fourth term of the sequence.

T4 = T3+T2/2

T4 = 14+8/2

T4 = 22/2

T4 = 11 (This is also an integer)

We will proceed to check the value of fifth term of the sequence.

T5 = T4+T3/2

T4 = 11+14/2

T4 = 25/2

T4 = 12.5 (This is not an integer)

This shows that the value of the first term in the sequence that is not an integer is 12.5