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andrey2020 [161]
2 years ago
5

How do you find the sum of the first 25 terms in a sequence?

Mathematics
2 answers:
BARSIC [14]2 years ago
8 0

Hey!

-----------------------------------------------

Explanation and Answer:

Find the difference between 2 points and see if the sequence is proportional. Then just keep adding till you get to the 25th sequence.

Let's say the sequence is 3,5,7,9,11. We subtract 2 points and we get 2. Each number is +3. After adding we get 50 as the 25th term.

-----------------------------------------------

Hope This Helped! Good Luck!

Stels [109]2 years ago
7 0

Answer:

Step-by-step explanation:

It's very necessary to find whether the given sequence is arithmetic or geometric.

In Arithmetic sequence every successive term has a common difference and in geometric sequence every successive term shows a common ratio.

Example of Arithmetic sequence:

1, 2, 3, 4, 5......  

2 - 1 = 1

3 - 2 = 1

common difference of 1.

Example of geometric sequence:

2, 4, 8, 16..........

\frac{4}{2}=2

\frac{8}{4}=2

Common ratio of 2

Now formula to calculate the sum of initial n terms of Arithmetic sequence

S_{n}=\frac{n}{2}[2a+(n-1)d]

where a = first term

n = number of terms to be added

d = common difference

Formula to calculate the sum of initial n terms of the Geometric sequence

S_{n}=\frac{a(r^{n} -1)}{r-1}

where a = first term of the sequence

n = number of terms to be added

r = common ratio

With help of these formula we can find the sum of first 25 terms of any sequence given.

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A new Community Center is being built in Oak Valley. The perimeter of the rectangular playing field is 382 yards. The length of
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Answer:

The width is 50 yards and the length is 141 yards.

Step-by-step explanation:

Let's call: L the length of the field and W the width of the field.

From the sentence, the perimeter of the rectangular playing field is 382 yards we can formulate the following equation:

2L + 2W = 382

Because the perimeter of a rectangle is the sum of two times the length with two times the width.

Then, from the sentence, the length of the field is 9 yards less than triple the width, we can formulate the following equation:

L = 3W - 9

So, replacing this last equation on the first one and solving for W, we get:

2L + 2W = 382

2(3W - 9) + 2W = 382

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8W = 382 + 18

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Replacing W by 50 on the following equation, we get:

L = 3W - 9

L = 3(50) - 9

L = 141

So, the width of the rectangular field is 50 yards and the length is 141 yards.

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