In reference to patterns there is a process of getting from one term to another or to finding a certain term in the pattern. first two words ru

There is no question asked, and the statement is incomplete, but this describes Series and Sequence. They are usually arithmetic or geometric progressions. A set of numbers are written to follow a particular pattern, when the pattern is clear, one can find any number of the sequence or series.

For example, consider the sequence below (Arithmetic Progression)

2, 4, 6, 8, ...

This sequence has a particular pattern.

The first term of the sequence is

a = 2

The common difference d, which is the difference between any two consecutive terms is

d = 2

The nth term, which is the formula that defines every single term of the sequence is given as

Tn = a + (n - 1)d

Check

T1 = a = 2

T2 = 2 + 2 = 4

T3 = 2 + 2(2) = 6

T4 = 2 + 2(3) = 8

T20 = 2 + 2(19) = 40

And so on.

Geometric progression

2, 4, 8, 16, 32, etc

First term, a = 2

Common ratio r, is the division of a particular number by the number preceding it.

r = 4/2 = 8/4 = 16/8 = 32/16 = 2

The nth term is given as

Sn = ar^(n-1)

S1 = a = 2

S2 = 2×2 = 4

S3 = 2×2^(2) = 8

S4 = 2×2^(3) = 16

S5 = 2×2^(4) = 32

S20 = 2×2^(19) = 1048576

And so on.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form