First row, the answer on the left , -5 3/4 - 4 2/3
FIRST FIND THE THE FIRST AND SECOND DIFFERENCES ON THE GIVEN SEQUENCE OF NUMBERS. FOR EXAMPLE IF YOU ARE GIVEN THIS SEQUENCE 2,4,6,8............AND YOU ARE ASKED TO FIND THE GENERAL FORMULA.... STEP 1:FIND THE FIRST DIFFERENCE BY SUBTRACTING THE FIRST TERM FROM THE SECOND TERM,AND THE SECOND FROM THE THIRD AND SO ON. STEP 2:FIND THE SECOND DIFFERENCE BY APPLYING STEP 1 TO THE ANSWERS OBTAINED.EG 4-2=2,6-4=2,8-6=2 THEREFORE THE SECOND DIFFERENCE WILL BE 2-2=0,2-2=0 STEP 3:DIVIDE THE SECOND DIFFERENCE BY 2 TO GET THE VALUE OF (A). STEP 4:WRITE 3a-b=the first term of the first term of the first difference which is the difference between 4 and 2.and solve for the value of b.3(0)-b=2 therefore b=-2 STEP 5:FIND THE VALUE OF c BY term 1=a=b=c
![\sf \bf {\boxed {\mathbb {GIVEN:}}}](https://tex.z-dn.net/?f=%5Csf%20%5Cbf%20%7B%5Cboxed%20%7B%5Cmathbb%20%7BGIVEN%3A%7D%7D%7D)
Sum of three consecutive odd integers = ![27](https://tex.z-dn.net/?f=27)
![\sf \bf {\boxed {\mathbb {TO\:FIND:}}}](https://tex.z-dn.net/?f=%5Csf%20%5Cbf%20%7B%5Cboxed%20%7B%5Cmathbb%20%7BTO%5C%3AFIND%3A%7D%7D%7D)
The values of the three integers.
![\sf \bf {\boxed {\mathbb {SOLUTION:}}}](https://tex.z-dn.net/?f=%5Csf%20%5Cbf%20%7B%5Cboxed%20%7B%5Cmathbb%20%7BSOLUTION%3A%7D%7D%7D)
![\sf\purple{The\:three\:consecutive \:odd\:integers\:are\:7,\:9\:and\:11.}](https://tex.z-dn.net/?f=%5Csf%5Cpurple%7BThe%5C%3Athree%5C%3Aconsecutive%20%5C%3Aodd%5C%3Aintegers%5C%3Aare%5C%3A7%2C%5C%3A9%5C%3Aand%5C%3A11.%7D)
![\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}](https://tex.z-dn.net/?f=%5Csf%20%5Cbf%20%7B%5Cboxed%20%7B%5Cmathbb%20%7BSTEP-BY-STEP%5C%3A%5C%3AEXPLANATION%3A%7D%7D%7D)
Let us assume the three consecutive odd integers to be
,
and
.
As per the condition, we have
![Sum \: \: of \: \: the \: \: three \: \: consecutive \: \: odd \: \: integers = 27](https://tex.z-dn.net/?f=Sum%20%5C%3A%20%20%5C%3A%20%20of%20%5C%3A%20%20%5C%3A%20%20the%20%20%5C%3A%20%20%5C%3A%20three%20%5C%3A%20%20%5C%3A%20%20consecutive%20%5C%3A%20%20%5C%3A%20%20odd%20%5C%3A%20%20%5C%3A%20%20integers%20%20%3D%2027)
![➺ \: x + (x + 2) + (x + 4) = 27](https://tex.z-dn.net/?f=%E2%9E%BA%20%5C%3A%20x%20%2B%20%28x%20%2B%202%29%20%2B%20%28x%20%2B%204%29%20%3D%2027)
![➺ \: x + x + 2 + x + 4 = 27](https://tex.z-dn.net/?f=%E2%9E%BA%20%5C%3A%20x%20%2B%20x%20%2B%202%20%2B%20x%20%2B%204%20%3D%2027)
Now, collect the like terms.
![➺ \: (x + x + x) + (2 + 4) = 27](https://tex.z-dn.net/?f=%E2%9E%BA%20%5C%3A%20%28x%20%2B%20x%20%2B%20x%29%20%2B%20%282%20%2B%204%29%20%3D%2027)
![➺ \: 3x + 6 = 27](https://tex.z-dn.net/?f=%E2%9E%BA%20%5C%3A%203x%20%2B%206%20%3D%2027)
![➺ \: 3x = 27 - 6](https://tex.z-dn.net/?f=%E2%9E%BA%20%5C%3A%203x%20%3D%2027%20-%206)
![➺ \: 3x = 21](https://tex.z-dn.net/?f=%E2%9E%BA%20%5C%3A%203x%20%3D%2021)
![➺ \: x = \frac{21}{3} \\](https://tex.z-dn.net/?f=%E2%9E%BA%20%5C%3A%20x%20%3D%20%20%5Cfrac%7B21%7D%7B3%7D%20%5C%5C)
![➺ \: x = 7](https://tex.z-dn.net/?f=%E2%9E%BA%20%5C%3A%20x%20%3D%207)
Therefore, the three consecutive odd integers whose sum is
are
,
and
respectively.
![\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}](https://tex.z-dn.net/?f=%5Csf%20%5Cbf%20%7B%5Cboxed%20%7B%5Cmathbb%20%7BTO%5C%3AVERIFY%20%3A%7D%7D%7D)
![⇢ 7 + 9 + 11 = 27](https://tex.z-dn.net/?f=%E2%87%A2%207%20%2B%209%20%2B%2011%20%3D%2027)
![⇢ 27 = 27](https://tex.z-dn.net/?f=%E2%87%A2%2027%20%3D%2027)
⇢ L. H. S. = R. H. S.
![\sf\blue{Hence\:verified.}](https://tex.z-dn.net/?f=%5Csf%5Cblue%7BHence%5C%3Averified.%7D)
![\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}](https://tex.z-dn.net/?f=%5Cred%7B%5Clarge%5Cqquad%20%5Cqquad%20%5Cunderline%7B%20%5Cpmb%7B%7B%20%5Cmathbb%7B%20%5Cmaltese%20%5C%3A%20%5C%3A%20Mystique35%E3%83%85%7D%7D%7D%7D%7D)
Area=length x width
A=10x(3/2 x + 1/2 y).
Now Distribute...
A=30x^2/2 + 10xy/2)
Now simplify fractions...
A=15x^2 + 5xy= 125
So I believe your answer is D)