Consider the arithmetic sequence 3,8,13,18 find S15

Mathematics

1 answer:

lora16 [44]2 years ago

3 0

Answer:

This is an arithmetic sequence since there is a common difference between each term. In this case, adding

to the previous term in the sequence gives the next term. In other words,

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Arithmetic Sequence:

This is the formula of an arithmetic sequence.

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Substitute in the values of

and

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Simplify each term.

Tap for more steps...

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Subtract

from

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Step-by-step explanation:

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Solve photo question, please. Mathematics.

skelet666 [1.2K]

Slope point form:
We need the slope "m" and a point (x₀,y₀)
y-y₀=m(x-x₀)

1)
we calculate the slope "m".
Given two points:
(x₁,y₁)
(x₂,y₂)
the slope "m" is:
m=(y₂-y₁) / (x₂-x₁)

In this case:
(4,10)
(6,11)
m=(11-10) / (6-4)=1/2

Now, we calculate the solpe point form.
(4,10)
m=1/2

y-y₀=m(x-x₀)
y-10=(1/2)(x-4)

we make the standard form
y-10=x/2 - 2

Lowest common multiple=2

2y-20=x-4
-x+2y=-4+20
-x+2y=16

Answer: -x+2y=16

3 0

3 years ago

Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15.

Naya [18.7K]

It's a geometric sequence.

$4,-12,36,... \\ \\
a_1=4 \\
r=\frac{a_2}{a_1}=\frac{-12}{4}=-3 \\ \\
a_n=a_1 \times r^{n-1} \\
a_n=4 \times (-3)^{n-1} \\
a_n=4 \times (-3)^{-1} \times (-3)^n \\
a_n=4 \times (-\frac{1}{3}) \times (-3)^n \\
a_n=-\frac{4}{3}(-3)^n$

It's the sum for term 4 through term 15.

$\boxed{ \sum\limits_{n=4}^{15} (\frac{4}{3}(-3)^n)}$