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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 geometric progression has a third term of 20 and a sum of infinity which is 3 times the first term. Find the first term ​
Anna007 [38]

Answer: the first term is 45

Step-by-step explanation:

Step 1: The formular for the nth term is ar^n-1 and since we're solving for the third term ar^3-1 = ar² which is equal to 20

So ar²= 20 and we make this equation i

Step 2: the formular for the sum of infinity is Sn = a/(1-r) and according the question the sum of infinity is equals to 3 *A ( A means the first term)

Further simplification gives us

3a= a/(1-r)

We simplify Futher by multiplying both sides by (1-r)

3a.(1-r) = a/(1-r).(1-r)

3a(1-r)=a

= 3a-3ar=a

Make 3ar the subject of the formula

3ar= 2a and lets make this equation (ii)

Step 3: From the first equation since ar²=20, let's make a the subject of the formula by dividing both sides by r²

Ar²/r² = 20/r²

A=20/r²lets make this equation (iii)

Step 4: subtitle a as 20/r² into equation (ii)

Since 3ar=2a

Then 3.(20/r²).r = 2. 20/r²

= (60/r²) .r = 40/r²

60/r = 40/r2

Multiplying both sides by r² gives us

60r = 40

Divide both sides by 20 gives us

= 3r= 2

Divide both sides by 3 gives us

= r = 2/3

Step 5: substitute r for 2/3 in equation i

ar²= 20

a. (2/3)2 = 20

= a.4/9 = 20

= 4a = 180

= a = 180/4

a = 45

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Solve for X kinda confused i don’t know what to do!!
sweet [91]

Answer:

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