Question

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

A(n) = 12 + (n-1)(3)

12, 21, 39

0, 9, 27

12, 24, 42

3, 24, 27

Answer 1

12, 21, 39 is the sequence given the given rule. Just plug in n=1, 4, 10 to evaluate each term.

Answer 2

12, 21, 39

Explanation:

Arithmetic sequence described by this rule in the question is :

A(n) = 12 + (n-1)(3)

a. Finding the first term

n = 1

A(n) = 12 + (n-1)(3)

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

A(1) = 12 + (0)(3)

A(1) = 12 + 0

A(1) = 12

Therefore the first term = 12.

b. Finding the fourth term

n = 4

A(n) = 12 + (n-1)(3)

A(4) = 12 + ( 4 - 1)(3)

A(4) = 12 + (3)(3)

A(4) = 12 + 9

A(4) = 21

Therefore the fourth term = 21

c. Finding the tenth term

n = 10

A(n) = 12 + (n-1)(3)

A(10) = 12 + ( 10- 1)(3)

A(10) = 12 + (9)(3)

A(10) = 12 + 27

A(10) = 39

Therefore the tenth term = 39

The first term = 12, the fourth term = 21 and the tenth term = 39