What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term of 3?

1 answer:

ioda3 years ago

6 0

In mathematics, number sequences are classified into three types: arithmetic progression, geometric progression and harmonic progression. Arithmetic sequences have a common difference, geometric sequences have a common ration, while harmonic progression is just the reciprocal of the arithmetic progression.

The first term of the arithmetic sequence is 5, followed by three. Therefore, the common difference is, 3-5 = -2. You use these values to the derived formulas for arithmetic progression. One of these formulas is

An = A1 + (n-1)d
where
An is the nth term in the sequence
A1 is the first term of the sequence
n is the totla number of terms within the sequence
d is the common difference.

In this problem, A1 = 5 and d=2. Substituting to the equation,

An = 5 + (-2)(n-1)
An = 5 - 2(n-1), where n should be more than 1. In order for it to become a sequence, it should contain more than one term.

So, the answer is letter D.

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PLEASE HELP HURRY!!!!!!!

Charra [1.4K]

As it has been given that $x=4+5i$ , $y=2-9i$ .

We need to find the value of the following:

(i) $4x-y$ , substituting the value of 'x' and 'y' in the expression, we get:

$4(4+5i)-(2-9i)=4\times 4+4\times 5i-2+9i=16+20i-2+9i$

$=14+29i$

So, $4x-y=14+29i$

(ii) $-x+3y$ , substituting the value of 'x' and 'y' in the expression, we get:

$-(4+5i)+3(2-9i)=-4-5i+3\times 2-3 \times 9i=-4-5i+6-27i$

$=2-32i$

So, $-x+3y=2-32i$

(iii) $x \times y$ , we need to substitute the value of 'x' and 'y' in the expression, for this, we can use distributive property of multiplication that says,