Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.

A (n) = - 6 + (n-1) (6)

6, 18, 54

-6, 12, 48

0, 18, 54

-6, 18, 54

-6,12 and 48.

Step-by-step explanation:

A (n) = - 6 + (n-1) (6)

This is the the nth term.

The first term is obtained when we use n = 1:-

First term A (1) = - 6 + (1 - 1) (6) = - 6 + 0

= - 6.

To find the fourth term we replace n by 4:

A (4) = - 6 + (4 - 1) (6)

= - 6 + 18

= 12.

In a similar way the 10th term

= - 6 + (10-1) (6)

= - 6 + 54

= 48.

Simplify:

A (n) = - 6 + (n - 1) (6) = - 6 + (n) (6) + (-1) (6) = - 6 + 6n - 6 = 6n - 12

Put n = 1, n = 4 and n = 10 to the expression:

A (1) = 6 (1) - 12 = 6 - 12 = - 6

A (4) = 6 (4) - 12 = 24 - 12 = 12

A (10) = 6 (10) - 12 = 60 - 12 = 48

Answer:first term = - 6, fourth term = 12 and tenth term = 48.-6, 12, 48