Question

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.

Answer 1

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                    $\sum_{n=4}^{15} 5(-2)^{n-1}$  

What is sequence ?

Sequence is collection of  numbers with some pattern .

Given sequence

$a_{1}=5\\\\a_{2}=-10\\\\\\a_{3}=20$

We can see that

$\frac{a_1}{a_2}=\frac{-10}{5}=-2$

and

$\frac{a_2}{a_3}=\frac{20}{-10}=-2$

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

Now $n^{th}$  term of this Geometric progression can be written as

$T_{n}= 5\times(-2)^{n-1}$

So summation of 15 terms can be written as

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

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                    $\sum_{n=4}^{15} 5(-2)^{n-1}$  

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