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Travka [436]
3 years ago
10

Find the sum of the first 30 terms of the equation below: an=4n+1

Mathematics
2 answers:
Katen [24]3 years ago
8 0

Answer:

1,890 is the sum of the first 30 terms of the equation .

Step-by-step explanation:

a_n=4n+1

if , n = 1

a_1=4\times 1+1=5

If, n = 2

a_2=4\times 2+1=9

If, n = 3

a_3=4\times 3+1=13

The arithmetic sequence comes out to be:

5, 9, 13........

a = 5

d = a_2=a_1=9-5=4

The sum of first 30 terms is given by:

S_n=\frac{n}{2}\times (2a+(n-1)d)

S_{30}=\frac{30}{2}\times (2\times 5+(30-1)\times 4)

S_{30}=1,890

1,890 is the sum of the first 30 terms of the equation .

Alex73 [517]3 years ago
6 0
Let n = 30

We are actually looking for a_30.

a_30 = 4(30) + 1

a_30 = 120 + 1

a_30 = 121

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If the function "f(x) = lxl-3" were translated five units down the graph, g(x) would be lxl-8.

We must be familiar with function transformation and different forms of transformation in order to properly understand the question. When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects" to create a new function. For instance, by simply pushing the graph of the function g(x) = x2 up by 7 units, the graph of the function f(x) = x2 + 7 is generated. It is advantageous to convert a function since it saves us from having to create a new function from begin. Function transformations typically fall into one of three categories: 1. 2nd translation 3. dilation Reflection

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When the curve changes, "the function" shifts upward or downward. By doing this, a function of the form y = f(x) is transformed into f(x) ± k, where k stands for the vertical translation. In this case, the function moves up by k units if k > 0.

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The curve in the given problem goes down by 5 units, so k = 5. Which is a vertical translation scenario. Consequently, y = f(x) becomes f(x) - k = g(x) and g(x) = f(x) - k = lxl-3 -5 = lxl - 8.

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Answer:

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angle QRS is same as (2x + 3) because it is an isosceles triangle

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