Answered

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Sum numbers of a given Geometric Sequence:
The formula I used is: Sn=a1((1 - r^n) / (1 - r))
Where r=the common ratio
a1=first term

Example:
(15 5s)
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

so:
S15 = 5((1 - 1^15) / (1 - 1))
S15 = 5((1 - 1)/(1 - 1))

but (1-1)/(1-1) will give me undefined so Sn=undefined?

Main question:
How to sum this kind of sequence using the formula.

Sagot :

Wynliviaidn

Answer and step-by-step explanation:

To find the sum of the terms of a sequence where all the terms are the same, you can't use the formula for the geometric sequence either it's finite or infinite.

If you use it, when r = 1 the answer will always be undefined because the denominator of the formula must not be equal to 0.

You can use the formula for the arithmetic sequence because a sequence with the same terms can also be an arithmetic sequence.

The formula for the arithmetic sequence is:

[tex]sn = \frac{n(a1 + an)}{2} [/tex]

Let's try using your example to find the sum of the sequence.

Example:

(15 5's)

5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

The common difference of the given sequence is 0 because if you subtract 5 from 5 the answer will always be 0.

Let's find the sum of the 15 terms by substituting the values to the formula.

[tex] \\ s15 = \frac{15(5 + 5)}{2} \\ \\ s15 = \frac{150}{2} = 75[/tex]

You can check it by adding all the given terms manually or just multiplying 5 by 15.

5 × 15 = 75

Therefore, you can only use the arithmetic sequence formula to find the sum of that kind of sequence.

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