Mathematics: Calculate s75 for the arithmetic sequence defined by

Calculate s75 for the arithmetic sequence defined

Ответ:

ashleyprescot05

10.03.2022

The value of $\rm S_{75}$ is -675 and this can be determined by using the formula of the sum of n terms in the arithmetic sequence and the given data.

Given :

$\rm a_n= 67-2n$ --- (1)

The following steps can be used in order to determine the value of $\rm S_{75}$ :

Step 1 - Substitute the value of (n = 1) in the expression (1).

$\rm a_1= 67-2(1)= 65$

Step 2 - Substitute the value of (n = 75) in the expression (1).

$\rm a_{75}= 67-2(75)= -83$

Step 3 - Now, the formula of sum in an arithmetic sequence is given below:

$\rm S_n=\dfrac{a_1+a_n}{2}\times n$

where n is the total number of terms, $\rm a_1$ is the first term, and $\rm a_n$ is the last term.

Step 4 - Substitute the values of the known terms in the above expression.

$\rm S_{75}=\dfrac{65-83}{2}\times 75$

Step 5 - Simply the above expression.

$\rm S_{75} = -675$

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Ответ:

craincrew5239

10.03.2022

Mathematics

The formula of a sum of an arithmetic sequence:

$S_n=\dfrac{a_1+a_n}{2}\cdot n$

We have n = 75 and a_n=67-2n .

Calculate the first and seventy-fifth term:

$a_1=67-2(1)=67-2=65\\\\a_{75}=67-2(75)=67-150=-83$

Substitute:

$S_{75}=\dfrac{65+(-83)}{2}\cdot75=\dfrac{-18}{2}\cdot75=-9\cdot75=-675$

-675

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Ответ:

AIhunter2884

03.04.2021

Mathematics

Step-by-step explanation:

Hey there!

Here;

Given is; angle AEB = 88°

angle AEB + angle AED = 180° { being linear pair}

88° + angle AED = 180°

angle AED = 180° - 88°

Therefore, angle AED = 92°

Therefore, answer is Option C.

Hope it helps...

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