Question

What is the 6th term of the A.P. 12, 9, 6, ...​

Answer 1

Answer:

A.P. = 12, 9, 6, ...

1st term (a) = 12

2nd term (b) = 9

n = 6

Cd = 2nd term - 1st term

= 9 - 12

= -3

6th term = a+(n-1)d

= 12 + (6-1)(-3)

= 12 + ( 5× -3)

= 12 + (-15)

= 12 - 15

= -3

Therefore , 6th term = -3

Answer 2

-3 is the sixth term of the A.P. 12, 9, 6...

Step-by-step explanation:

Arithmetic progression is a progression in which every term after the first term (a) is obtained by adding a constant value, called the common difference (d). The $n^{th}$ term is given by the equation: $a_{n}= a+(n-1)d$

First term, $a= 12$

Common difference=

$d= 9-12\\d= -3$

The  term is given by

⇒ $a_{6}= a+(6-1)(-3)$

⇒ $a_{6}= 12+(6-1)(-3)$

⇒ $a_{6}= 12+(5)(-3)$

⇒ $a_{6}= 12-15$

⇒$a_{6}= -3$

∴ -3 is the sixth term of the A.P. 12, 9, 6...