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What is the sum of the geometric sequence −3, 18, −108, … if there are 7 terms? −719,835 −119,973 119,973 719,835

Respuesta :

anchitthawi
Sn = a1 (1-r^n) / (1-r)
= -3 (1- (-6)^7) / (1-(-6))
= -3 (1-(-279936)) / 7
= -3 (279937) / 7
= -119,973 #

Answer:

The correct option is:  -119,973

Step-by-step explanation:

Geometric sequence:    -3,  18,  -108, ..............

First term, [tex]a_{1}= -3[/tex]

Common ratio, [tex]r= \frac{a_{2}}{a_{1}} =\frac{18}{-3}= -6[/tex]

Number of terms in the sequence, [tex]n= 7[/tex]

Sum of n terms:    [tex]S_{n}= \frac{a_{1}(1- r^n)}{1-r}[/tex]

So, sum of 7 terms,

[tex]S_{7}= \frac{-3[1-(-6)^7]}{1-(-6)} = \frac{-3(1+279936)}{1+6}=\frac{-839811}{7}=-119973[/tex]

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