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emmainna [20.7K]
3 years ago
5

Develop an explicit formula in terms of n for the nth term of the following sequence:

Mathematics
1 answer:
nalin [4]3 years ago
4 0
<h2>Answer with explanation:</h2>

The given sequence :  0,4,18,48,100,180,......

We can write the terms of the sequence as :

\text{Ist term }:a_1=1(1^2-1)=0\\\\\text{IInd term }: a_2=2^2(2-1)=4(2-1)=4\\\\\text{IIIrd term }:a_3=3^2(3-1)=9(2)=18\\\\\text{IVth term }:a_4=4^2(4-1)=(16)(3)=48\\\\\text{Vth term }:a_5=5^2(5-1)=25(4)=100\\\\\text{VIth term }:a_6=6^2(6-1)=36(5)=180

From the above presentation of the terms, the explicit formula in terms of n for the nth term will be :-

a_n=n^2(n-1)

Put n= 7 , we get

a_7=7^2(7-1)=49(6)=294

Therefore, the seventh term of the given sequence = 294

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On a number line, the distance from zero to -8 to 8?<br> 8^2=64<br> |-8|=8<br> |-8|=-8<br> 0+8=8
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Answer:

Step-by-step explanation:

Lateral surface area of the triangular prism = Perimeter of the triangular base × Height

By applying Pythagoras theorem in ΔABC,

AC² = AB² + BC²

(34)² = (16)² + BC²

BC = \sqrt{1156-256}

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Perimeter of the triangular base = AB + BC + AC

                                                      = 16 + 30 + 34

                                                      = 80 in

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Total Surface area = Lateral surface area + 2(Surface area of the triangular base)

Surface area of the triangular base = \frac{1}{2}(\text{Base})(\text{Height})

                                                           = \frac{1}{2}(30)(16)

                                                           = 240 in²

Total surface area = 1760 + 2(240)

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Volume = Area of the triangular base × Height

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Answer:

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Step-by-step explanation:

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