Respuesta :
Answer:
22.6
Step-by-step explanation:
Given:
- a = 3
- a + a₆ = 20
Find the value of a₆:
[tex]\implies a+a_6=20[/tex]
[tex]\implies a_6=20-a[/tex]
[tex]\implies a_6=20-3[/tex]
[tex]\implies a_6=17[/tex]
Therefore:
- a = 3
- a₆ = 17
General form of an arithmetic sequence:
[tex]\boxed{a_n=a+(n-1)d}[/tex]
Where:
- [tex]a_n[/tex] is the nth term.
- a is the first term.
- d is the common difference between terms.
- n is the position of the term.
Substitute a = 3 and a₆ = 17 into the formula and solve for d:
[tex]\begin{aligned}\implies a_6=3+(6-1)d&=17\\3+5d&=17\\5d&=14\\d&=2.8\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\implies a_n=3+(n-1)2.8[/tex]
[tex]\implies a_n=3+2.8n-2.8[/tex]
[tex]\implies a_n=2.8n+0.2[/tex]
To find the 8th term, substitute n = 8 into the equation for the nth term:
[tex]\implies a_8=2.8(8)+0.2=22.6[/tex]