It should look like a parabola with the part below x-axis cut off. the left side starts from x=-1, opening upward & to the left, the right side starts from x=2, opening upward and to the right.

7 0

3 years ago

18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Ksenya-84 [330]

$a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}$

$S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525$

8 0

3 years ago

A mapping diagram showing a relation, using arrows, between input and output for the following ordered pairs: (negative 3, negat

VladimirAG [237]

Answer:

The correct option is A) {x | x = –5, –3, 1, 2, 6}

Step-by-step explanation:

Consider the provided diagram.

Here the left side represents the input (X) values and the right side represents the output (Y) values.

The domain refers to the set of possible input values.

Now consider the provided figure, the set of input value is:

{x | x = –5, –3, 1, 2, 6}

Hence, the correct option is A) {x | x = –5, –3, 1, 2, 6}

5 0

3 years ago

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