Identify the pattern and find the next number in the pattern.
0.4, 1.2, 3.6, 10.8

32.4

Step-by-step explanation:

This is a geometric progression

The formula for geometric progression Tₙ= arⁿ⁻¹

Where a = first term

r = common ratio

n = number of term

First we need to find the common ratio

Common ratio = Tₙ/Tₙ₋₁

Using the 3rd term

Common ratio = T₃ /T₃₋₁

Common ratio = T₃ /T₂

T₃ = 3.6

T₂ = 1.2

Common ratio = 3.6/1.2

Common ratio = 3

From the question, we are to find it's 5th term

The formula is already given as :

Tₙ= arⁿ⁻¹

here a = first term

r = common ratio

n = number of terms

Where

a = 0.4

r = 3

n = 5

Therefore,

T₅ = 0.4 × 3⁵⁻¹

T₅ = 0.4 × 3⁴

T₅= 0.4 × 81

T₅ = 32.4

The next number in the pattern is 32.4

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl