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

12, 21, 39

Step-by-step 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

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.