Question

Given the sequence in the table, which of the following represents the sum for term 5 through term 11 in sigma notation? (1 point)

a an
1 2
2 −10
3 50

Answer 1

Answer:

Given sequence in the table is a Geometric sequence and The sum for term 5 through term 11 in sigma notation is given by:

$\sum_{n=5} ^{\111} 2(-5)^n^-^1$

                                                                                                                     

Step-by-step explanation:

Geometric sequence - it is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio

here the given terms :

a1 = 2, a2 = -10, a3 = 50

you can see it is a geometric sequence as the ratio is constant  $\frac{a2}{a1}{=}\frac{a3}{a2}{=}{-5}$

now the nth term for geometric sequence :

$a_{n} {=}{a}{r}^{n-1}$

here,

• a = first term.

• r = common ratio of the given terms.

• n = number of terms in geometric sequence.

now substituting the given values in the expression,

$a_{n} {=}{2}{{(}-5}{)}^{n-1}$

we have to find the sum from term 5 to term 11,

therefore using sigma notation and putting n= 5 and n=11 at the below and above the sigma respectively,

$\sum_{n=5} ^{\111} 2(-5)^n^-^1$    

learn more about geometric progression at brainly.com/question/4853032

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