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skad [1K]
4 years ago
9

Find the 80th term of the following arithmetic sequence

Mathematics
1 answer:
lina2011 [118]4 years ago
7 0

Answer:

The 80th term would be 647

Step-by-step explanation:

In order to find the 80th term, you need to find the rule for the sequence. You'll notice that the numbers are going up by 8. Since there is no 0th term, the first term would be 8 more than the base.

15 - 8 = 7

Therefore the base is 7. As a result, you can model the sequence as:

An = 8n + 7

In which n is the number in the sequence. Now knowing this, we can plug in 80 and get the answer.

An = 8n + 7

An = 8(80) + 7

An = 640 + 7

An = 647

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4 0
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\left\{\begin{array}{ccc}2x+3y=68&|\cdot(-15)\\30x+11y=112\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-30x-45y=-1020\\30x+11y=112\end{array}\right}\\.\ \ \ \ \ \ \ -34y=-908\ \ \ |:(-34)\\\\.\ \ \ \ \ \ \ \ \ \ \  y=\dfrac{908}{34}\to y=\dfrac{454}{17}\\\\2x+3\cdot\dfrac{454}{17}=68\ \ \ \ |\cdot17\\\\34x+1362=1156\ \ \ \ |-1362\\34x=-206\ \ \ \ |:34\\\\x=-\dfrac{206}{34}\to x=-\dfrac{103}{17}\\\\  \left\{\begin{array}{ccc}x=-\dfrac{103}{17}\\\\y=\dfrac{454}{17}\end{array}\right
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