Question

For some integer n, the first, the third and the fifth terms of an arithmetic sequence are respectively 3n, 5n – 6, and 11n + 8. What is the fourth term?

Answer 1

a₄=8n+1= -39.

Explanation:

1) if a₁=3n; a₃=5n-6 and a₅=11n+8, then it is possible to calculate the difference according to 0.5(a₅-a₃)=0.5(a₃-a₁). Then

2) 0.5(11n+8-5n+6)=0.5(5n-6-3n); ⇔ 6n+14=2n-6; ⇔ n= -5.

3) if n=-5, then the 4th term is:

`a_4=(a_5+a_3)/(2); \ = > \ a_4=(11n+8+5n-6)/(2)=8n+1;`

or a₄=-39.