The first two numbers in a sequence h are h(1)=2 and h(2)=6

If h is an arithmetic sequence, write a definition for the nth term of h explain or show your reasoning.

Respuesta :

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The nth term of the arithmetic series can be defined as hₙ = 4n - 2.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

The nth term of an arithmetic sequence is given by the formula,

aₙ = a₁ + (n-1)d

Since the first term of the arithmetic sequence is 2, while the difference is 4. Therefore, the definition for the nth term of arithmetic sequence,h can be written as,

hₙ = 2 + (n-1)4

hₙ = 2 + 4n -4

hₙ = 4n - 2

Hence, the nth term of the arithmetic series can be defined as hₙ = 4n - 2.

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