Ammarosidn
Answered

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Here, what would be the answer to these two pre-calculus problems? Work would be appreciated.
(I was hoping to give alot of points for this question - since there are 2 - but I'm still unsure about how everything works in Brainly. It shouldn't be too bad to answer though)

Here What Would Be The Answer To These Two Precalculus Problems Work Would Be AppreciatedI Was Hoping To Give Alot Of Points For This Question Since There Are 2 class=

Sagot :

AGboiiidn

[tex] \large\underline \bold{{SOLUTION\:1}}[/tex]

We noticed that the given questions are arithmetic sequence. Hence , We will use the sum of arithmetic sequence formula.

First , Finding for the common difference by subtracting the terms.

[tex]\sf{A_2-A_1=5-1 = 4}[/tex]

[tex]\sf{A_3-A_2=9-5=4}[/tex]

By the first 2 tries , We knew that the common difference is 4. And Going back to our equation:

Given that: [tex]\textsf{$A_1=1$ , n=10 , d=4}[/tex]

[tex]\longmapsto\sf{S_n = \frac{n}{2}[2(A_1)+(n-1)d]}[/tex]

[tex]\longmapsto\sf{S_{10} = \frac{10}{2}[2(1)+(10-1)4]}[/tex]

[tex]\longmapsto\sf{S_{10} = 5[2+(9)4]]}[/tex]

[tex]\longmapsto\sf{S_{10} = 5[2+36]}[/tex]

[tex]\longmapsto\sf{S_{10} = 5(38)}[/tex]

[tex]\longmapsto\boxed{\sf{S_{10} = 190}}\longleftarrow\rm{Answer}[/tex]

[tex] \large\underline \bold{{SOLUTION\:2}}[/tex]

Given that the terms are -15 to 40. By subtracting we will get a total of 56 terms including 0. Then , We knew that their common difference is 1 because -15,-14,-13...,40.

[tex]\sf{A_2-A_1=-14-(-15) = 1}[/tex]

[tex]\sf{A_3-A_2=-13-(-14) = 1}[/tex]

Now , Going back to the formula:

Given that: [tex]\textsf{$A_1=-15$ , n=56 , d=1}[/tex]

[tex]\longmapsto\sf{S_n = \frac{n}{2}[2A_1+(n-1)d]}[/tex]

[tex]\longmapsto\sf{S_{56} = \frac{56}{2}[2(-15)+(56-1)1]}[/tex]

[tex]\longmapsto\sf{S_{56} = 28[2(-15)+(55)1]}[/tex]

[tex]\longmapsto\sf{S_{56} = 28[-30+55]}[/tex]

[tex]\longmapsto\sf{S_{56} = 28(25)}[/tex]

[tex]\longmapsto\boxed{\sf{S_{56} = 700}}\longleftarrow\rm{Answer}[/tex]

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