Question

In an Arithmetic Progression (AP), the first
term is 3, and the sum of the first and the sixth
terms is 20. What is the 8th term

Answer 1

Answer:

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

Answer 2

Answer:

22.6

Step-by-step explanation:

Given:

• a = 3

• a + a₆ = 20

Find the value of a₆:

$\implies a+a_6=20$

$\implies a_6=20-a$

$\implies a_6=20-3$

$\implies a_6=17$

Therefore:

• a = 3

• a₆ = 17

General form of an arithmetic sequence:

$\boxed{a_n=a+(n-1)d}$

Where:

• $a_n$ 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:

$\begin{aligned}\implies a_6=3+(6-1)d&=17\\3+5d&=17\\5d&=14\\d&=2.8\end{aligned}$

Therefore, the equation for the nth term is:

$\implies a_n=3+(n-1)2.8$

$\implies a_n=3+2.8n-2.8$

$\implies a_n=2.8n+0.2$

To find the 8th term, substitute n = 8 into the equation for the nth term:

$\implies a_8=2.8(8)+0.2=22.6$