Question

1, How did you find the sum of the given geometric sequence?

2,What do you think will be the easiest way to find the sum of a given geometric sequence?​

Answer 1

Answer:

1 For r≠1 r ≠ 1 , the sum of the first n terms of a geometric series is given by the formula s=a1−rn1−r s = a 1 − r n 1 − r .

Step-by-step explanation:

2

To find the sum of a finite geometric series, use the formula, Sn=a1(1−rn)1−r,r≠1 , where n is the number of terms, a1 is the first term and r is the common ratio

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Answer 2

Given: The following questions.

To find:

1, How did you find the sum of the given geometric sequence?  

2,What do you think will be the easiest way to find the sum of a given geometric sequence?​

Solution:

1. We find the sum of the given geometric sequence by using the formula

sum = [a(1-rⁿ)]/(1-r)  

2. The easiest way to find the sum of a given geometric sequence is the one metioned in part (1).

A geometric sequence is a sequence of numbers in which every adjacent number are in the same proportion with one another.

1.

In order to find the sum of a geometric sequence, the following formula can be used.

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

The above formula can be used provided that the value of r is not equal to 1. Here, a is the first term, r is the common ratio and n is the term to be calculated.

2.

The easiest way to find the sum of a given geometric sequence is the way that is mentioned in the part (1) of the question. This is because it is much easier to use the formula and calculate the sum of the terms rather than actually finding all the terms and adding them.

Therefore,

1. We find the sum of the given geometric sequence by using the formula

sum = [a(1-rⁿ)]/(1-r)  

2. The easiest way to find the sum of a given geometric sequence is the one metioned in part (1).