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Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15. N an 1 4 2 −12 3 36 the summation of 4 times negative 3 n, from n equals 4 to 15 the summation of 4 times negative 3 n, from n equals 1 to 15 the summation of 4 times negative 3 to the n minus 1 power, from n equals 1 to 15 the summation of 4 times negative 3 to the n minus 1 power, from n equals 4 to 15.

Respuesta :

By applying basic property of Geometric progression we can say that sum of 15 terms of a sequence whose first three terms are 5, -10 and 2 is                    [tex]\sum_{n=4}^{15} 5(-2)^{n-1}$[/tex]  

What is sequence ?

Sequence is collection of  numbers with some pattern .

Given sequence

[tex]a_{1}=5\\\\a_{2}=-10\\\\\\a_{3}=20[/tex]

We can see that

[tex]\frac{a_1}{a_2}=\frac{-10}{5}=-2\\[/tex]

and

[tex]\frac{a_2}{a_3}=\frac{20}{-10}=-2\\[/tex]

Hence we can say that given sequence is Geometric progression whose first term is 5 and common ratio is -2

Now [tex]n^{th}[/tex]  term of this Geometric progression can be written as

[tex]T_{n}= 5\times(-2)^{n-1}[/tex]

So summation of 15 terms can be written as

[tex]\sum_{n=4}^{15} T_{n}\\\\$\\$\sum_{n=4}^{15} 5(-2)^{n-1}$[/tex]

By applying basic property of Geometric progression we can say that sum of 15 terms of a sequence whose first three terms are 5, -10 and 2 is                    [tex]\sum_{n=4}^{15} 5(-2)^{n-1}$[/tex]  

To learn more about Geometric progression visit : https://brainly.com/question/14320920

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