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ryzh [129]
3 years ago
5

If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁?PLEASE HELP ME​

Mathematics
1 answer:
katen-ka-za [31]3 years ago
3 0

\text{nth term of  an arithmetic sequence,}\\\\a_n = a_1 + (n-1)d\\\\a_4 = a_1 +3d=107~~~......(i)\\ \\a_8=a_1+7d = 191~~~......(ii)\\\\\\\text{(ii) -(i):}\\\\~~~~~~a_1+7d-a_1-3d = 191 -107\\\\\implies 4d = 84\\\\\implies d = \dfrac{84}4\\\\\implies d= 21\\\\\text{Substitute d= 21  in eq~(i):}\\ \\~~~~~ a_1 +3(21) =  107\\\\\implies a_1 + 63 = 107\\\\\implies a_1 = 107-63\\\\\implies a_1 =44

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Jerome found the lengths of each side of triangle QRS as shown, but did not simplify his answers. Simplify the lengths of each s
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Answer:

QR = 6.0033

QS = 8.22

RS = 6.0033

QRS is isosceles

Step-by-step explanation:

Given

See attachment for complete question

From the attachment, we have the following parametersQR = \sqrt{(-3-0)^2+(-5.2-0)^2}

QR = \sqrt{9+27.04}

QS = \sqrt{(-3-5)^2+(-5.2-(-3.322))^2}

QS = \sqrt{64+3.53} = \sqrt{67.53

RS = \sqrt{(0-5)^2 + (0 - (-3.322))^2}

RS = \sqrt{(25 + 11.04}

Solving further, we have:

QR = \sqrt{9+27.04}

QR = \sqrt{36.04}

QR = 6.0033

QS = \sqrt{64+3.53} = \sqrt{67.53}

QS = 8.22

RS = \sqrt{25 + 11.04}

RS = \sqrt{36.04}

RS = 6.0033

From the calculations;

RS = QR = 6.0033

<em>This means that: QRS is isosceles</em>

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