Respuesta :

Answer:

The 8th term of the AP= 113/5 or 22.6

Ver imagen kennethkwakye918
Ver imagen kennethkwakye918

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]

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