Pls help I’ll give you 35 points I need help on theses problems

Mathematics

1 answer:

Nataliya [291]1 year ago

5 0

Answer:

I attached my answer. please, check it.

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Please help!! Write the sum using summation notation, assuming the suggested pattern continues. -9 - 4 + 1 + 6 + ... + 66

fiasKO [112]

$r=-4-(-9)=-4+9=5 \\ \\ a_{1}=-9 \\ \\ a_{n}=66 \\ \\ a_{n}=a_{1}+(n-1)r \\ \\ -9+5(n-1)=66 \\ \\ -9+5n-5=66 \\ \\ 5n-14=66 \\ \\ 5n=80 \\ \\ n=16 \\ \\ S_{n}= \frac{a_{1}+a_{n}}{2} *n \\ \\ S_{n}= \frac{-9+66}{2}*16=57*8=456$

4 0

2 years ago

Give a rule for finding the first of four consecutive odd integers if you know the sum of the four integers.

Artemon [7]

This ones a bit of a trick question, since whether the integers are even or odd doesn't really matter. What does matter, is that consecutive odd integers are 2 numbers apart (as are consecutive even integers).

So again, if the first of the odd integers is the variable n

the consecutive odd integers after it can be written as:

n+2 , n+4, etc...

So the sum of four consecutive odd integers can be written as:

sum = n + (n+2) + (n+4) + (n+6)

Simplify:

sum = 4n + 12

And finally rearrange to solve for n:

$\frac{sum-12}{4}$ = n