Ammarosidn
Answered

Makakuha ng mabilis at eksaktong mga sagot sa IDNStudy.com. Makakuha ng impormasyon mula sa aming mga eksperto, na nagbibigay ng detalyadong sagot sa lahat ng iyong mga tanong.

Here, what would be the answer to this pre-calculus problem? Work would be appreciated.

Here What Would Be The Answer To This Precalculus Problem Work Would Be Appreciated class=

Sagot :

AGboiiidn

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

Using the Arithmetic Sequence Formula.

[tex]\sf{A_n=A_1+(n-1)d}[/tex]

[tex]\sf{A_n=A_1+(n-1)\frac{3}{4}}[/tex]

[tex]\sf{A_n=A_1+(\frac{3n}{4}-\frac{3}{4})}[/tex]

Now , All we need to do is to find the First term

[tex]\sf{A_1-\frac{3}{4}=10}[/tex]

[tex]\sf{A_1=10+\frac{3}{4}}[/tex]

[tex]\sf{A_=\frac{43}{4}}[/tex]

Thus , the sequence looks like this

[tex]\sf{A_n=A_1+(n-1)d}[/tex]

[tex]\sf{A_1=\frac{43}{4}+(n-1)\frac{3}{4}}[/tex]

Where the common difference is [tex]\boxed{\sf{\frac{3}{4}}}[/tex]

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

Using the substitution method:

  • First term

[tex]\sf{a_n=\frac{3}{4}n-10}[/tex]

[tex]\sf{a_1=\frac{3}{4}(1)-10}[/tex]

[tex]\sf{a_1=\frac{3}{4}-10}[/tex]

[tex]\sf{a_1=\frac{3}{4}n-10}[/tex]

[tex]\sf{a_1=\frac{-37}{4}}[/tex]

  • Second term

[tex]\sf{a_n=\frac{3}{4}n-10}[/tex]

[tex]\sf{a_2=\frac{3}{4}(2)-10}[/tex]

[tex]\sf{a_2=\frac{3}{2}-10}[/tex]

[tex]\sf{a_2=\frac{-17}{2}}[/tex]

  • Third term

[tex]\sf{a_n=\frac{3}{4}n-10}[/tex]

[tex]\sf{a_3=\frac{3}{4}(3)-10}[/tex]

[tex]\sf{a_3=\frac{9}{4}-10}[/tex]

[tex]\sf{a_3=\frac{-31}{4}}[/tex]

To find their common difference , We will subtract each of them.

[tex]\sf{A_2-A_1=\frac{-17}{2}-(\frac{-37}{4})=\boxed{\frac{3}{4}}}[/tex]

[tex]\sf{A_3-A_2=\frac{-31}{4}-(\frac{-17}{2})=\boxed{\frac{3}{4}}}[/tex]

[tex] \large\underline{ \bold{ANSWER}}[/tex]

  • Yes , it is an arithmetic sequence with a common difference of 3/4