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

Hey!

Explanation and

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!

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..........

Common ratio of 2

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

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

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.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c

answer: #1 ads up by 8 and i don't know #2